Lord Darkain said:

Not legal.  Clearly stated in the basic rulebook:

Choose a Faction: Players agree on which
factions to control. One player controls Rebels
while the other controls Imperials. If players
cannot agree, randomly assign factions.
All components belonging to a player’s own
faction are considered friendly, and all
components belonging to his opponent’s faction
are considered enemy.

And from the Tournament Rules PDF:

Each player must build one squad for use in an X-Wing tournament. The squad-building rules described
in this section supersede the squad-building rules described in the X-Wing rulebook.
The maximum squad points for each player is 100 points. A squad cannot exceed 100 points, though it
may contain fewer than 100 points.
Each player may choose to field either a Rebel or Imperial squad, as tournament seeding ignores the
player’s faction.

Nowhere are players given permission to mix ships from different factions into the same squad.  For a wacky, different game at home, sure.  For any kind of organized play, totally not allowed.

Jim

There were a couple of Star Wars comics where Han Solo faced a pirate captain who had stolen a Star Destroyer.

His team used every kind of fighter and created some crossbreed ships when there weren' enough repair parts.

A scenario like that might be fun.

I would love to have the brother-in-law's flying together as a flight pair

Wedge in his X-Wing and Soontir in his Tie Interceptor.

A bit off topic but,

the 'Crossbreed' title reminded me of the "Uglies" from the old X-Wing book series.  That was the name that Rogue Squadron (or was it the Wraiths?) gave to the cobbled together ships of pirates and bandits; TIE cockpits with Y-Wing engines and such.  Would be neat to see and play with something like that. 

Someone beat you to it:   http://www.afewmaneuvers.com/forums/viewtopic.php?f=26&t=47

Theres nothing to stop you using mixed squads if your gaming group allows it.

(Tournaments and rules-wise, as others said is a no-no)

Fluff-wise, theres plenty mentions of rebel pilots using TIES (usually Imperial pilots who have just went AWOL and took their fighters with them.)

(Though how they manage that without a Hyperdrive is anyones guess! lol)