The sinks may be smelling for a couple of reasons:
- You have a leak in the sink trap - all of the ater is draining from the trap which allows sewer gases to escape through the drain. Since the problem is with two sinks - this is not the likely culprit.
- You have an improperly vented waste line. (Or the vent may be clogged.) When the water from another fixture empties into the drain stack, it creates a vacuum. If the venting is clear, the vacuum will suck air from the outside of the house. If the venting is not clear, the vacuum will try to suck the air from the path of least resistance - the sink traps. This sucks all of the water out of the traps too - which lets the gases escape.
This is probably happening after you send a large amount of water down the drain in a short period of time. That may be a toilet, a washing machine, could be a dishwasher - although not likely since it's both the kitchen and bathroom sink - depends on how the waste line is hooked up.
How to solve this? Chances are you need a plumber. (You can fix it yourself - but it's not a simple fix. If what I wrote above makes sense, you may feel that you can tackle it yourself.) The good news is, it shouldn't be too big of a job.
To do it yourself - find out what else drains into the same line as these sinks. Send some water down the drains from these other fixtures - if you hear a gurgling in the sink, that's what's causing it. BUT - the problem is not that fixture itself, but the venting of it - it's either improper or clogged.
Another way to solve it is to run water in the sinks a couple times a day to refill the traps.