So I decided to try this combination with a few house rules, as there are no official rules yet and some areas are quite debatable.
I played on the Alien board with Firefly board under it, only Serenity part being visible. I randomly chose Hadley's Hope location and three objectives, the two and the third one being put in secret under the first one - the S.O.S.
I have to also mention my starting cards - I chose randomly one of the Firefly crew, Inara, and the following four being the main characters: Mal, Zoe, Wash and River. I also chose starting cards from Firefly to form my starting deck, with one more Misbehave and two more Shineys than normally, so that the game would be harder and thus more interesting. That's why I also decided to include 6 Side Jobs/Drones in my deck, two for each Objective/Episode (3 Side Jobs + 3 Drones to be exact).
Also, I put two strike decks on the board, one from Alien game for Alien enemies and one from Firefly from Firefly enemies. To make the ship strikes matter more and make the game more exciting, I decided for the following house rule: When the enemy from Alien game would strike, I will roll a die and on a role of 1 I will draw a Ship strike instead of a Crew strike.
I also randomly selected characters for my character deck - 2 characters from both games. I ended up with Sister Ripley, Navigator Lambert, Jayne and Book. I used 5 Browncoats and no Sergeants as my.
Let's start with the first objective - The S.O.S. Everything was going smoothly, Inara killed a couple of eggs, were able to draft a couple of Navigator Lamberts with card draw, which was a good combo. I should also mention my Coordinate house rule which was suggested on the Legendary games forums for solo play - I could set aside one Coordinate card for next turn and play it as Coordinate. This rule is IMHO much better that the rule for solo play suggested in the Firefly rulebook.
Anyway, I succeeded with fulfilling the first objective and because there were two parts of the S.O.S., I decided to take take two credits for them and with the credits I healed, as there were no interesting ship upgrades available. Then I revealed the second objective - Heart of Gold, Episode 13 from Firefly. So I just put the cards under the remaining cards in the Alien stack, ending with the Inevitable card, and continued play. With the help of Coordination I successfully drafted Jayne's Vera (as many strikes as strikes on characters in my HQ) and it was really insane with Sister Ripley - Ultimate Sacrifice being in my HQ (5 strikes) and Book's Last Rites (allowing to put a card from my discard pile back on top of my deck). With the help of this combo I killed all enemies quite easily but unfortunately Nandi didn't survive due to some nasty Range attacks. I should also mention that there was an Event and Hazard after fulfilling the first Objective - I just discarded them and added another card from the hive(as the currect obejctive wasn't an Alien one) and it worked quite well, I think I will stick to this house rule in future.
With the second objective finished quite easily, 3 credits spent on ship upgrades, I revealed the last objective - A Perfect Organism. I filled the Complex with 4 cards (as I removed all cards from the second Firefly objective from play), then started playing. Aliens started to be really strong and poor Inara was soon in trouble. The Perfect Organism jumped into the combat zone just after Airlock controls were put into place. Another Alien jumped int the combat zone. Having already several strikes on her, she rolled the dice three times and for the first time there was a Ship strike. Those aliens were obviously big enough to make some damage to Firefly. Inara fought valiantly, even managed to push the Perfect Organism into the Airlock and managed to injure it - 6 damage. But she needed 10 and that was the end. With 2 ship strikes on Serenity, she finally died but she had no regrets - it was an exciting life and an exciting game.
All house rules worked quite well, I cannot think of anything I would like to change for my next game. I'm looking forward to playing the combination of these two games with more players.