I don't know of rides where they will let you stand so close that you can get on the ride when your DH disembarks. It seems to me that they will not even let you enter the line with a child who does not meet the height requirement. (This could depend, of course, on the CM at the time.)
We did exactly what you are asking about. We produced the child in question

to the CM at the fastpass lane. They gave us a "rider swap" pass for us to use; re-entry was the FP lane and we were rarely in line for very long waiting for the other spouse and older child (for rides on which she met the height requirement).
I would
NOT recommend "just" getting a FP, as there are many attractions for which you can obtain a FP that have no height restriction. Once you have a FP, you can't get another one until the time on your original FP has arrived. We found it much more efficient to get a Rider Swap pass. That way, you can use your FP for Peter Pan, for example, with the younger kids, if your DH becomes addicted to Splash or Space Mtn
If it is extremely crowded, you could just get one FP, let's say for EE. Have your DH ride EE on the FP and get you a Rider Swap pass. If it's really crowded, you would then be able to get a FP on your ticket for Dinosaur! (or whatever, you get the idea

) and then reverse the process.
The PPs have all listed great places to go with your kids while you and your DH use Rider Swap. Additionally, at Animal Kingdom, we found that if you head toward Kali River Rapids from EE, there are a few exhibits with animals (seems I remember some orangutans or the like) along the pathway.
Have fun!