I encountered some problems yesterday posting my reply, but it looks like Jim K9YC had the same idea as me - you are most likely plugging a 3-connector audio cable into a 4-connector audio jack on your laptop. You can buy an inexpensive Y cable that will plug into your laptop's 4-connector TRRS jack and provide for you a 3-connector TRS jack for stereo headphones and a 2-connector TS jack for microphone. You then can use a 3-connector male-to-male stereo cable from this Y cable to the phones connection on the KX3 and either a 2-connector or 3-connector male-to-male audio cable to the Mic connection.
Here's an example of the product I'm describing, but there are many similar products available:
Hopefully this, and the other advice about time synchronization will get you on your way. I agree that using an external USB sound card might give you greater dynamic range (if you buy the right one), but I kind of favor the Y cable approach because it is simpler/lower tech.
