I think that if your city has barracks then you should be able to 'build' a unit in the barracks, and still be making improvements to the city. How would you split shields, well, 50,50 except for a wartime economy. In which case, it is 100% to barracks (kind of like it is now, as you cannot build other items).
If your barracks is empty, then it all goes to the city improvement, and vice versa!
still simple, and you get to do both!
to take this idea further, I think once you build a factory, you should be able to build 2 units at a time. Whatchathink?