Can you play the Crisis Expansion's Crisis Mode with the core game and Heroes Unite combined?
As per BGG
James Cheng:

One of the option rules for combining and playing with both set mix up is to alternate your game with two separate decks. So you can play two game with each half of the combined deck. The second game will have a little more knowledge about what you might expect.

Richard Brady of Cryptozoic chimes in

At Cryptozoic, if we want to play with mixed sets... we generally mix all the cards up from the first two (and future!) sets and then count out about 115 or so cards to be our main deck. Sometimes you get some scary games with a lot of Villain cards but for the most part it's worked out pretty cool.
Otherwise, I'd suggest making a deck list of your favorite cards but make sure it's somewhere between 110-140. If you go above 140 it actually gets fairly easy, though we've made our own weird variants that use over that amount. We have never gone over 150 as far as I can remember.

John Galietta III:

If I recall my rulebook perusal correctly, it recommends that if you wish to customize the decks, use 25 cards per player. With 1-3 player games this is a little small, so I'd say no smaller than 100 cards. But just a random 100+ cards seems a little random for my tastes. You don't get as much of the synergy you normally would.
I usually keep my main decks separate. If I want to play using both sets, we use both decks separately, using 2 line ups. With the rules that A) you can only buy/gain/affect one line-up per turn, and B) when you buy/gain a card from the line-up, destroy the card in the second line-up in the same spot. There was a file about this variant in one of the forums.
I'd say for that, if you wanted to use the new main deck cards as well just mix 16 into each of the main decks. this variant wouldn't work very well in Crisis mode, though.

There's also this article on a supposed balance of combining the two decks. That might work as well.
In short while there are workarounds some of which are semi-official. There's no official method of combining. There are however many player suggested varients that should resolve the complexities.