I dunno. Is it a:
1) Human half-celestial half-dragon?;
2) A half-celestial dragon?; or
3) A half-dragon celestial?
I suspect you're asking about 1). Waving aside any doubts about the feasibility of such a creature*, I'd just add them together, which I believe would be a +6 based on DMG.
This includes adding together all the racial bonuses (+12 Str, +2 Dex, +6 Con, +4 Int, +4 Wis, +6 Cha), special attacks (spell-like abilities and breath weapon), +5 natural armor bonus to AC, low-light vision, darkvision to 60', all their immunities (acid, electricity, cold, disease, and one from a dragon, which better darn well be fire, plus a +4 Fort save vs. poison), the half-dragon's claw/claw/ bite and bigger hit die. That's a lot, and I can't imagine being able to convince the DM that it's anything less than MAYBE a +5 ECL, and probably +6.
For real fun, become celestial for the DR and SR, and arrange to get bitten by a weretiger and then get atoned. And, of course, since by this point you're the only one of your kind, it's possible you might wake up to find yourself a paragon. Sure, you'll never get XP again, and it's real expensive getting raised when you die, given that you'll have a lot fewer HD than the rest of the party, but it'll be fun! ;-) (And here's where access to one of the level-raising books would come in real handy...)
Though, be warned, if the DM hasn't thought of this already when you mention it, you'll start running into half-fiend half-dragons, who, for similar abilities, will have two more HD than you (since the two templates only add up to +4 CR).
* - The waving part of this will be...interesting, if you're looking to start play as a half-celestial half-dragon human. Perhaps you're the child of a Polymorphed ghaele eladrin and a polymorphed gold dragon, or you're the product of a Good Temple's secret breeding program to produce the Ultimate Paladin (tm). In play, either could be accomplished with a flexible enough DM and Strange Mysterious Rites.
Brad