This Instructable grew out of a response to a question by janmcevoy, who is contemplating joining two bicycles side-by-side for more riding stability when bringing home groceries by bicycle. It is really for her, but others may view and comment.
Shown is my bicycle on the left and my wife's bicycle on the right. If I were pairing two bicycles, I would pick two that are more similar, and would probably not use one with drop handlebars.
Step 1: Keep the bikes next to one another
Struts or braces can be used to pair two bikes in a side-by-side configuration. The green lines represent the location of bracing to keep the two bikes abreast of one another so one does not lead or lag behind the other. The bracing together with the chain stay forms a triangle, which is very rigid and a basic component of structural engineering.
If two bikes are to be paired like this, the bracing cannot interfere with the normal movement of the pedals, the feet, and the legs. This diagram assumes the rider will ride from the bike on the left. The bracing could be flipped if the rider were to be on the right side bike.
I would remove the crank and the chain on the bike not ridden. Not only does this lighten the bike, but it also offers more places to connect things.