01kipper: When a multiclass character levels up you get half the HitPoints of a single-class character of the same class. You get the Full con bonus (if applicable) on the first character class to reach that level, and no con bonus when the other class(es) reach that level.
So, for example, let's say you have a F/M level 1/1. When you advance to Fighter level 2 you will get 0.5*(1d10)hp + full con bonus. Then when you advance to Magic-User level 2 you will get 0.5*(1d4)hp + no con bonus.
kmonster: Not exactly true for the Gold Box games.
In other games than PoR double class characters get a total of the average HP the single classes would get rounded down, triple class characters can get even less total.
In Pools of Radiance 19 con is treated just like 18 but multiclass characters usually can get more HP than should be possible.
How the hitpoints at partial level ups are distributed doesn't always look logical, it seems as it was written directly into the code how many HP they should get for partial level ups, just try out a little.
From my old PoR notes about max HP at level up:
fighter/thief with 17-19 con: 7 as fighter, 5 as thief
fighter/mage with 17-18 con: 7 as fighter, 4 as mage
cleric/mage with 16 con: 5 as cleric, 4 as mage
cleric/fighter/mage with 18 con: 5 as fighter, 4 as cleric, 3 as mage
In later games multiclasses get far less HP, my 18 con cleric/fighter/mages in CoK couldn't get more than a sum of 9 HP for a level up in all 3 classes combined, no matter how I split the level up.
What about a F/M/T with a 14 con? Started at 5 HP, the thief level just kept giving 1 (although I didn't save scum as much as the fighter), and now the fighter level is giving 1-3. I've probably restarted it 40 times now. Haven't gotten to mage level but I'm wondering if it's going to be 3/1/1. Kinda crappy, but guess I'll manage. Bow mage it is.
Anyway, just wondering if someone else has some input on this. Otherwise ... this seems to be par for the course. Will update if anything changes on following levels.