Hi there, polymer chemist checking in.
This is in fact a very complicated question in its ramifications, and not one that really lends itself to picking up a textbook but I'll brute force an answer and tell you that no, you cannot simply melt any of these together and they will stay that way. Polymers are, on longer time scales, immiscible with one another if they are significantly different. Significant can even mean polyethylene and polypropylene, which are only different by a single carbon. Basically what happens on the micro-level is they seperate out like oil and water. This can takes minutes or months depending on what exactly is going on. This is a fundamental tenet of polymer chemistry. It also generally ruins the material properties of the mixture when they phase separate.
Different polymers can be covalently bound to one another. In that case, you will get nano-phase separation, which has its own unique properties, but this requires a strong knowledge of chemistry to understand and do correctly, and is not really what you are looking forward.
Now, you can laminate two polymers in a layer on top of one another, and they may stay nicely together in layers, since they are already phase separated. I am not an expert in that particular concept.
I'm sorry I can't help you more, but you are frankly asking questions about a difficult and subtle art that takes many years to learn. Making laminates is, in itself, a whole field within polymer chemistry.
You would be MUCH better off working with finding just one polymer that has the combination of properties you need, or perhaps using small molecule additives to adjust properties.