I'm in music clubs where we get lots of beginners every week: fiddlers. lap dulcimers, harmonicas, mandolines, and banjos. One group even gives free lessons on autoharps and dulcimers each week. Most of these insturments are designed to play lead, and not rythhm. With the mandoline and autoharp and guitar and banjo, we'll usually start with chords, rather than melodies. On the fiddle and harmonica and dulcimer, we'll start with the melody.
    Usually, these are two chord songs: D -A.
    My suggestion is to pick a few songs that are familiar to both of you. Usually, these are hymnns or old popular songs: Amazing Grace, You Are My Sunshine, Silent Night, I'll Fly Away, etc. Just decide what key that you're going to do these in beforehand; that way, you'll both start in the same place. The key here is choosing familiar melodies.
    One of the other advantages of picking very familiar tunes is that you widen the circle of people with whom you can jam. Just have fun! You'll both benefit a lot!!!!!