SMDs on bottom side of board with THT components?
You'll need to talk to your assembler, but this is not necessarily a problem. There are essentially five options:


Use pin-in-paste to install your through-hole parts.  This is where solder paste is stenciled onto through-hole pads, then the through-hole parts are installed into the paste-filled holes, and your PTH and SMT parts can all be soldered in one reflow pass.  The major downside is that the PTH parts have to be specifically designed to withstand this process which really limits your part options. The plastics used in many standard PTH connectors that are not designed for pin-in-paste will soften or completely melt at reflow temperatures.
Glue down the bottom side SMT components and wave solder them at the same time as the PTH parts.  This is usually used on high volume production of low-complexity boards (such as power supplies), and is not advisable for fine-pitch parts, large ceramic capacitors, or other mechanically/thermally sensitive parts.
Wave solder using masks and jigs to protect the SMT components.  This is highly dependent on the component placement, board geometry, and other factors.
Selective wave soldering, where a machine moves a small sort of fountain of molten solder around the board, so that through-hole parts can be soldered after all of the SMT parts have been installed.  This is an ad for a machine manufacturer, but it shows the process fairly well: https://www.youtube.com/watch?v=p-VImd2yW5s
Hand soldering.  Many assemblers have the equipment and personnel that make this a viable option for ~hundreds of boards, depending on complexity.  Sometimes this is simply the best option for really fiddly jobs, and a good assembler will often create fixtures or jigs to help ensure accurate assembly even with hand soldering.  It avoids the setup costs that the other processes require, so it's a good low-ish volume option.


Of course, additional process steps will increase the cost of assembling the board, but it's pretty common to have double-sided SMT and PTH on boards these days.