The main plot of your story is what keeps the reader coming back for more. If that suddenly grinds to a halt, you run the risk of losing the reader. Just how entertaining and important are these chapters?
- Could someone skip them and still enjoy the story?
- Is the reader likely to become frustrated that the story has suddenly stopped?
- Can the reader fill in the backgrounds/motivations for themselves?
- Do you really need to explain everything, and if you do: Why can't these sides of their characters be revealed in the main story?
If you still feel you need these chapters, then make sure that you present them as an actual subplot -- which is to say, a separate story that runs alongside the main one.
You use the word "subplot" in your title, but then describe something which sounds like vague disconnected chapters. If there's another story to be had here, then there's no reason to not run it in parallel with your main one. That's often extremely enjoyable for your readers (just about every TV show episode has several stories, for example, that aren't all necessarily connected).
It's worth remembering that the FLY episode of Breaking Bad stopped the main story to delve into the characters, and the reaction by a lot of fans was VERY negative -- despite the fact that the episode itself is actually very well written and directed. It's generally not a good idea just to stop and meander, and when TV shows do it it's usually because of budgetary constraints. (Plus, it's worth noting that the episode DID progress the main storyline, if only slightly.)
So be honest with yourself, and your readers, and ask yourself if these extra chapters are entertaining. If you really thought the answer was "yes", I'm pretty sure you wouldn't be asking your question, so maybe you can take the information from them and make it more interesting somehow.