As far as I can tell, megski, your problem is a lot simpler. (It remains to be seen whether usernamenumber got their problem resolved.) From what I can discern from the information you have provided the following are true:
(1) Your husband redeemed the Blood Dragon armour on his Gamertag on 'his' 360.
(2) When you play on 'his' 360, you get the Blood Dragon armour.
(3) You keep your saves on a USB stick so you can use them on a different 360.
(4) Problem occurs when you try to play Dragon Age on a different 360.
(5) You cannot download the Blood Dragon armour.
(6) You have your own Gamertag.
Some don't appreciate it but I will give an explanation as to why.(Having been insulted for giving explanations for why something doesn't work has left me rather apathetic to fellow gamers' plights.)
Dlcs follow consoles and Gamertags. Said dlc is on your husband's Gamertag, and that Gamertag is native to 'his' console. On that same console, you can access any dlc he has registered on his Gamertag on 'his' console. (It makes no sense for the same console to have several purchases of the same software.) On a different console you immediately lose such dlc sharing privileges.
The game also recognises what dlc is available to it. Having played on 'his' 360 your save games recognises that the Blood Dragon armour should be in the game regardless of what you have done with it. That is why the problem occurs for you.
Now addressing specific points: with regards to (5) you cannot download it on your Gamertag because it is not your dlc. Only your husband's Gamertag can do that.
Possible solutions.
(A) You mentioned having your own code for the Blood Dragon armour. Have you tried to redeem it? There is no harm in doing so to see if the system accepts it. It might be worth asking
EA support to see if they can activate a copy of the armour for you.
And if you do then you will have your own armour. This will not help with playing the other dlcs though. It also depends on whether you have any of the unlockable weapons from the other campaigns: if you do you still have a problem.
(

Is 'his' 360 always online?
I ask this because I believe there could be a work around if I understand how these things work, though a bit fiddly. It would require him to
recover his Gamertag on 'your' 360 whilst online; making all dlcs native to 'your' 360. This will enable you to access his dlcs. However, if he does this 'his' 360 will technically be bereft of his content; but if 'his' 360 is permanently, or close to it, online and he signs into his Gamertag he should be able to access his content.
© Making my (

suggestion defunct: you and your husband swap 360s.
(D) Not the most financially sensible, but one which the economy would thank you for, purchase all the dlcs yourself.
That's all I can think of for now.