A Template Class
Officially, this kind of “breakdown,” as you call it, is known as a “template class,” a concept pioneered in Savage Species. The idea is that you gain the powers of the template over the course of several levels, rather than all at once, to allow you to play lower-level monstrous characters. While a pretty simple idea (and massively better than the default ECL system), Savage Species itself is one of the most notorious books published for 3.x, and the random additional template classes that Wizards posted on their website from time to time often received even less oversight.
Your DM’s Version
We don’t have the details aside from the fact that you are, in fact, gaining Level Adjustment rather than HD. Your DM is correct that LA does not grant HD, so this is 8 levels in a row where you do not gain HD, base attack bonus, saves, or skills. This is a very serious problem. Even if he’s trying, your DM is going to have a hard time keeping you alive while you face opponents appropriate for your (and your comrades’) effective level.
I do not recommend that you do this. The vampire template was badly over-LA’d to begin with (like almost everything that has a positive LA; Wizards did not think players should choose monstrous races and so they chose LAs to discourage players from choosing them and to punish those that did), and depending on how this “breakdown” works, it could leave you even worse off than someone starting at ECL 9th with 1 HD. For example, the official template class certainly does that...
The Official Template Class
The official template class, posted online here, is problematic on a number of points. One, you lose your Constitution score slowly, over the course of a number of levels. This is awful because you do not get the d12 HD and immunity to Fortitude-targeting effects that form the “upsides” of being “Con –” until 7th level.
And once again, even more importantly, is the issue of LA +8 and how that’s not really viable. Potentially even worse since you have drastically-reduced Constitution. You basically gain almost all of the disadvantages first, and don’t gain the corresponding advantages. This probably is going to lead only to your destruction.
I cannot overstate how much I do not recommend this.
Oslecamo’s Template Class
Oslecamo, a member of a number of D&D message boards, has made an enormous project of creating an incredible number of monster and template classes. His vampire can be found here; note that it is in an entire subforum devoted to this project. His work is rather well-regarded, and I rather like his execution of the vampire. It has all of the classical weaknesses, all of the (excellent) Undead traits, and a number of Blood Powers that function off the Blood Charges that the vampire gains by drinking victims. Notably, every night the vampire needs a number of Blood Charges equal to his HD just to feed his hunger, so high-level vampires are strongly encouraged to maintain a stock of sycophants or followers who will allow him to drink their blood.
What I like most, though, is that the class is only 2 levels long. It’s built much more like a Prestige Class than as a template, and I think it dramatically improves it. It doesn’t have the myriad numerical bonuses associated with the official vampire template, but instead you get to be a normal character who is also a vampire.
This is much better design for a number of reasons, not least because templates’ ability score bonuses are often inappropriate. Level Adjustment plus too-high ability score bonuses makes the character too-good at some things (ability checks, save DCs) and too-weak at other things (its own saves, skill ranks, base attack bonus, and protections against things like sleep), which I personally have found to be very detrimental to the game.