If your requirements are simple, you can use bare Sendmail. It is not something I particularly recommend, but since you wanted to avoid mutt...
# Now that we actually concatenate two files (well, stdin and a file),
# we are no longer eligible for a Useless Use of Cat Award
( cat - body.html <<HERE
Subject: My subject
Mime-Version: 1.0
Content-type: multipart/related; boundary="foooobar"
--foooobar
Content-type: text/html
HERE
cat <<HERE
--foooobar
Content-type: image/png
Content-disposition: inline
Content-transfer-encoding: base64
HERE
base64 image.png
echo; echo '--foooobar--' ) | sendmail -oi $RECIPIENTS
I do wish there were a simple, standard utility for this, but alas, instead there are many, all more or less mutually incompatible and murky. Again, if you can use mutt, that's probably the most widely supported and standard tool you can hope for.