I have mentioned this before, but an old crusty accordion technician, who has been working on free reed instruments almost as long as melodicas have been in existence, told me that yes, melodicas are intended to be played monophonically. If you look at the music supplied with old Hohner melodicas over the years, it is limited to monophonic lead parts.
I find that the level of dissonant harmonics varies widely when playing intervals on a melodica, depending the interval and the quality of tuning of the melodica.
However, sometimes I consider this an positive attribute when playing the blues. A dirty, dissonant, distorted interval or chord from an old beat up melodica sometimes sounds really great in the right type of blues song. One of the tricks is to play the interval or chord quickly, as an accent. Or play it sustained if in fact you want a dissonant sound. I like some level of dissonance in music when done correctly.
Of course for many types of music, the dissonant harmonics of intervals are not welcome.
If you really want dissonance, try singing into the melodica as you are playing a note. You can feel the whole melodica vibrate in sympathy with your voice as your voice moves sharp, in tune, and flat of the note being played. At some points, your voice will set up a resonant vibration with the reed and body of the melodica and you will get wicked distortions. Yesterday I was doing this (playing and singing a note simultaneously) and when I played a new note on the melodica, it caused my voice to involuntarily rise, following the tone of the new note. This kind of blew me away as it hints at the close connection between air flow, air pressure, vibration, frequency, vocal chords, sound waves, melodica body, melodica reeds, etc. I am going to experiment more with this. Imagine a sax, oboe, or clarinet mouthpiece attached to a melodica! I think a Melodica World member already experimented with this. I remember hearing a haunting audio clip by a Melodica World member many months ago.