Point of View and Subplot

Do you think each significant character in your plot needs a subplot? 

I haven't really thought about it like this before, but I have been overdosing lately on a favourite author, and realised that one of the ways in which she creates a multi-layered plot, and also makes all her main characters three-dimensional, is by creating subplots that eventually collide with the main one.

Now, I have subplots. But they're not usually specifically targeted at a character like that. In my last novel (which is not ready for the light of day) the subplot belonged to the police officer investigating my main character's crime. Then there was a very lightweight little plot which doesn't deserve to be called a subplot, which just fleshed out Mr Love Interest a bit. But perhaps Mr Love Interest needed a bit more going on.

In my current work, there is a triangle of characters, who I will name (somewhat misleadingly, but tough, I'm not going for a synopsis here) Mrs Main, Love Interest 1 and Love Interest 2. The conflict is between Mrs Main and Love Interest 1, so he doesn't really have a subplot. There are side issues arising, which Mrs Main doesn't know about immediately, but they're still part of the main plot. Love Interest 2 is crucial to the main plot in every way, but doesn't have his own subplot. 

He has a backstory - career, family, failed engagement, hobbies - the lot. The relevant parts will be in the story. He is a point of view character - I have written scenes through his eyes.

But does he need a subplot of his own? Would it make him more believable? Or would it complicate the story too much? 

I feel as though the lack of one may be undermining an important convention in the kind of books I read (and want to write). 

There is another character who is also vital to the whole, and the threads of her story weave into the main, underpin it and provides a different voice, told in a different tense and person. She is also important, and brings texture to the whole....but I'm not sure her story can really be called a subplot, either. 

So is this story too slim? I'm a long way through to be having doubts, and I think I may have to plough on and just see...it has felt good so far, and it already needs serious pruning to make it a sensible length, so it isn't  as if it's flimsy in terms of length. But perhaps it lacks depth...

What do you think? Should all the main characters have a serious problem of their own going on 'on the side'?