diff --git a/swh/web/inbound_email/utils.py b/swh/web/inbound_email/utils.py
--- a/swh/web/inbound_email/utils.py
+++ b/swh/web/inbound_email/utils.py
@@ -180,6 +180,7 @@
 
     text_parts: List[bytes] = []
     fallback_parts: List[bytes] = []
+    all_parts: List[bytes] = []
 
     for part in message.walk():
         content_type = part.get_content_type()
@@ -190,15 +191,23 @@
             current_part = part.get_payload(decode=True).rstrip(b"\n")
             if current_part:
                 text_parts.append(current_part)
-        elif not text_parts and content_type == "text/html":
+                all_parts.append(current_part)
+        elif content_type == "text/html":
             current_part = part.get_payload(decode=True).rstrip(b"\n")
             if current_part:
                 fallback_parts.append(current_part)
-
-    if text_parts:
-        return max(text_parts, key=len)
-
-    if fallback_parts:
-        return max(fallback_parts, key=len)
+                all_parts.append(current_part)
+
+    assert message.get_content_maintype() == "multipart"
+    if message.get_content_subtype() == "alternative":
+        if text_parts:
+            return max(text_parts, key=len)
+
+        if fallback_parts:
+            return max(fallback_parts, key=len)
+    else:
+        # Handles multipart/mixed; but this should be an appropriate handling for
+        # other multipart formats
+        return b"".join(all_parts)
 
     return None
diff --git a/swh/web/tests/inbound_email/resources/multipart.eml b/swh/web/tests/inbound_email/resources/multipart_alternative.eml
rename from swh/web/tests/inbound_email/resources/multipart.eml
rename to swh/web/tests/inbound_email/resources/multipart_alternative.eml
diff --git a/swh/web/tests/inbound_email/resources/multipart_html_only.eml b/swh/web/tests/inbound_email/resources/multipart_alternative_html_only.eml
rename from swh/web/tests/inbound_email/resources/multipart_html_only.eml
rename to swh/web/tests/inbound_email/resources/multipart_alternative_html_only.eml
diff --git a/swh/web/tests/inbound_email/resources/multipart_text_only.eml b/swh/web/tests/inbound_email/resources/multipart_alternative_text_only.eml
rename from swh/web/tests/inbound_email/resources/multipart_text_only.eml
rename to swh/web/tests/inbound_email/resources/multipart_alternative_text_only.eml
diff --git a/swh/web/tests/inbound_email/resources/multipart_mixed.eml b/swh/web/tests/inbound_email/resources/multipart_mixed.eml
new file mode 100644
--- /dev/null
+++ b/swh/web/tests/inbound_email/resources/multipart_mixed.eml
@@ -0,0 +1,23 @@
+Return-Path: <test@example.com>
+Content-Type: multipart/mixed; boundary="------------BR6CvS06rj0369ladb31gYCL"
+Message-ID: <8318382c-b4d3-9239-0805-e8cff4b9187a@inria.fr>
+Date: Thu, 7 Apr 2022 10:30:36 +0200
+MIME-Version: 1.0
+User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:91.0) Gecko/20100101
+ Thunderbird/91.7.0
+Content-Language: en-US
+To: Test User <test@example.com>
+From: Test User <test@example.com>
+Subject: test email
+
+This is a multi-part message in MIME format.
+--------------BR6CvS06rj0369ladb31gYCL
+Content-Type: text/plain; charset=UTF-8; format=flowed
+Content-Transfer-Encoding: 7bit
+
+This is plain text
+
+--------------BR6CvS06rj0369ladb31gYCL
+Content-Type: text/html
+
+and <b>this is HTML</b>
diff --git a/swh/web/tests/inbound_email/resources/multipart_mixed2.eml b/swh/web/tests/inbound_email/resources/multipart_mixed2.eml
new file mode 100644
--- /dev/null
+++ b/swh/web/tests/inbound_email/resources/multipart_mixed2.eml
@@ -0,0 +1,25 @@
+Return-Path: <test@example.com>
+Content-Type: multipart/mixed; boundary="------------BR6CvS06rj0369ladb31gYCL"
+Message-ID: <8318382c-b4d3-9239-0805-e8cff4b9187a@inria.fr>
+Date: Thu, 7 Apr 2022 10:30:36 +0200
+MIME-Version: 1.0
+User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:91.0) Gecko/20100101
+ Thunderbird/91.7.0
+Content-Language: en-US
+To: Test User <test@example.com>
+From: Test User <test@example.com>
+Subject: test email
+
+This is a multi-part message in MIME format.
+--------------BR6CvS06rj0369ladb31gYCL
+Content-Type: text/plain; charset=UTF-8; format=flowed
+Content-Transfer-Encoding: 7bit
+
+This is plain text
+
+--------------BR6CvS06rj0369ladb31gYCL
+Content-Type: text/plain; charset=UTF-8; format=flowed
+Content-Transfer-Encoding: 7bit
+
+and this is more text
+
diff --git a/swh/web/tests/inbound_email/resources/multipart_mixed_text_only.eml b/swh/web/tests/inbound_email/resources/multipart_mixed_text_only.eml
new file mode 100644
--- /dev/null
+++ b/swh/web/tests/inbound_email/resources/multipart_mixed_text_only.eml
@@ -0,0 +1,36 @@
+Return-Path: <test@example.com>
+Content-Type: multipart/mixed; boundary="------------BR6CvS06rj0369ladb31gYCL"
+Message-ID: <8318382c-b4d3-9239-0805-e8cff4b9187a@inria.fr>
+Date: Thu, 7 Apr 2022 10:30:36 +0200
+MIME-Version: 1.0
+User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:91.0) Gecko/20100101
+ Thunderbird/91.7.0
+Content-Language: en-US
+To: Test User <test@example.com>
+From: Test User <test@example.com>
+Subject: test email
+
+This is a multi-part message in MIME format.
+--------------BR6CvS06rj0369ladb31gYCL
+Content-Type: text/plain; charset=UTF-8; format=flowed
+Content-Transfer-Encoding: 7bit
+
+My test email
+--------------BR6CvS06rj0369ladb31gYCL
+Content-Type: text/html; charset=UTF-8; name="attachment.html"
+Content-Disposition: attachment; filename="attachment.html"
+Content-Transfer-Encoding: base64
+
+PGh0bWw+CiAgICA8aGVhZD4KICAgICAgICA8dGl0bGU+VGhpcyBpcyBhbiBleGFtcGxlIEhU
+TUwgYXR0YWNobWVudDwvdGl0bGU+CiAgICA8L2hlYWQ+CiAgICA8Ym9keT4KICAgICAgICA8
+cD5UaGlzIGlzIGFuIGV4YW1wbGUgSFRNTCBhdHRhY2htZW50PC9wPgogICAgPC9ib2R5Pgo8
+L2h0bWw+Cg==
+--------------BR6CvS06rj0369ladb31gYCL
+Content-Type: text/plain; charset=UTF-8; name="attachment.txt"
+Content-Disposition: attachment; filename="attachment.txt"
+Content-Transfer-Encoding: base64
+
+VGhpcyBpcyBhIHRleHQgYXR0YWNobWVudC4K
+
+--------------BR6CvS06rj0369ladb31gYCL--
+
diff --git a/swh/web/tests/inbound_email/test_utils.py b/swh/web/tests/inbound_email/test_utils.py
--- a/swh/web/tests/inbound_email/test_utils.py
+++ b/swh/web/tests/inbound_email/test_utils.py
@@ -260,22 +260,44 @@
             id="plaintext",
         ),
         pytest.param(
-            "multipart.eml",
+            "multipart_alternative.eml",
             [b"*Multipart email.*\n\n-- \nTest User"],
             [],
-            id="multipart",
+            id="multipart_alternative",
         ),
         pytest.param(
-            "multipart_html_only.eml",
+            "multipart_alternative_html_only.eml",
             [b"<html>", b"<b>Multipart email (a much longer html part).</b>"],
             [b"<b>Multipart email (short html part)</b>"],
-            id="multipart_html_only",
+            id="multipart_alternative_html_only",
         ),
         pytest.param(
-            "multipart_text_only.eml",
+            "multipart_alternative_text_only.eml",
             [b"*Multipart email, but a longer text part.*\n\n--\nTest User"],
             [],
-            id="multipart_text_only",
+            id="multipart_alternative_text_only",
+        ),
+        pytest.param(
+            "multipart_mixed.eml",
+            [b"This is plain text", b"and <b>this is HTML</b>"],
+            [b"This is a multi-part message in MIME format."],
+            id="multipart_mixed",
+        ),
+        pytest.param(
+            "multipart_mixed2.eml",
+            [b"This is plain text", b"and this is more text"],
+            [b"This is a multi-part message in MIME format."],
+            id="multipart_mixed2",
+        ),
+        pytest.param(
+            "multipart_mixed_text_only.eml",
+            [b"My test email"],
+            [
+                b"HTML attachment",
+                b"text attachment",
+                b"This is a multi-part message in MIME format.",
+            ],
+            id="multipart_mixed_text_only",
         ),
     ),
 )