PCB Design: Through hole components on both sides?
If you plan on hand soldering, through hole parts on both sides is doable.

The issue with manufacturing though is it is difficult to flow solder with through hole parts on both sides. You can do it, but you may need to do a lot of conformal solder masking, once for each side, and that is labor intensive and expensive. Some fab houses have specialized equipment that allow more selective soldering, but there are setup costs involved in that, so unless it's a big run, the cost per board factor is significant.

As with all double side populated boards though, the space saving is limited by the routability. On a dense board, using the other side does not buy you as much space as you would imagine and adds considerable cost. 

Further, since through hole parts are already effectively double sided, the leads poke through to the other side, you cant re-use the spots where things poke through, and you need to be able to see those leads to solder them. So again, it saves you very little.

Using SMT instead of through hole is a better way to reduce the size. 

If the board is still too big with both side populated SMT, your next best bet is to split the board into two with suitable connectors so you can make it a sandwich. That can be designed with both parts on a single panel and manufactured as a single board and split and assembled later. Another alternative is to build it on a flexible circuit and fold it up.