I think this is an interesting idea. It's not actually that different from the 3e approach... or is it?
It's the "progresses independently" part that makes it unlike 3E. So if a fighter pays the 5,000 premium to be able to start getting wizard XP, he can advance as fighter or wizard, each using the same chart, but not stacking the levels.
I didn't talk about it in the original, but I was also thinking that the players/table would have some leeway in how they split the points. Perhaps you must put at least 10%, 20%, 25% in each class every time you get points, but the remainder you can split or put all into one class, as you choose. How high you set this minimum percentage effectively caps how many classes you can take--and reduces your flexibility the more you take. Then the table can also adjust the 5,000 XP premium. By adjusting those two variables, you dictate a lot about how much multiclassing is worth it, and how far it can be pushed.
One of the nice things about 3E multiclassing is that every player gets to set the mix of classes how they want, but the 3E way isn't the only way to handle that. And like the 1E/2E way, the 3E way suffers in that it isn't easy to adjust, as each level in any class makes the next one harder. Using my proposed system, if you want to put a 50/50, 60/40, or 75/25 mix in two classes, you'll get results that about match what a casual player would expect.
BTW, the big disadvantage of my proposal for traditional D&D play is that once you get near the level cap, it becomes inordinately advantagous to spread out. This becomes especially true (and happens sooner), if there are a lot of levels to take. The more levels, the less the premium means at the upper end. Now, this doesn't bother me that much, because if some heretofore single-class Fighter, at level 15, decides it is worth it to knock out five levels of wizard, even with the premium, then I see that as more rounding out the character than adding raw power--especially since there is a limit on how many classes he can so take. But I must acknowledge that such a character growth dynamic is a bit off in traditional D&D, and more like what you would get with Hero or GURPS or Runequest or such. It's nothing that can't be house ruled around (e.g. force early multiclassing for any character that wants it), but the house rules are not very elegant.
Edit: Now reading Zustier's post above, I see he anticipates me. But I'll let my stuff stand as a different wording, slightly different take on some of the same concepts and issues.
Certainly I would treat stacking elements as gestalt--i.e. you get the hit points, weapon attack bonus, etc.--each of any single class you choose. It has to be that way in this system, because of how the levels progress. If taking levels in a wizard is knocking a bit off your fighter XP, and thus costing you a level or three in your best class for hit points, then the effect needs teeth. Otherwise, there is no cost. Not having exponential character advancement tables, a 50/50 character will fall further behind than 1 level versus a single class. In fact, this system works better in Next than it would in any previous D&D edition, because the bounded accuracy means that such a character might still only be penalized a point of attack bonus. The slow advancement of numbers means that you can let such level differences stand.