SMD Elements on the back of THT
Yes, you can do this

In general, there is no problem with putting components on both sides of the board, in the same place.  If you had a two (or more) layer board, you's probably want to put a ground or power plane between them, but you can't do that with a single layer board.  So you should watch out for a fast digital chip interfering with an analog circuit.  It would be inadvisable, for example, to put a microcontroller on one side and a high input impedance buffer on the other. But putting decoupling caps opposite the chip is probably a good plan.

If you want to meet CE requirements for noise immunity and emissions, you will have difficulty with this type of design, and a two layer board would help a lot.  For hobby use, what you have looks fine.