^ Normally that is the correct approach especially (and particularly) in a bank of batteries, but in a starter-deepcycle scenario like many of us run, that's impractical and the reason why I prefer to either invert the incoming power and run a mains charger (no real connection between the two batteries, and the way that I do it at the moment) or use an isolating charger system like the C-Tek D250S.
The reason for not connecting batteries of different chemistry is simple. Starter batteries, designed for very brief periods of super-high current, don't enjoy being drained below 50% and are often not charged up over 75% of their actual capacity (long drives and bench charging of course change this).
Deep cycle applications generally don't see anything near the rush of current, typical draws usually are below 10A (fridge from 4-5-7.5A, lights of 2A tops with LED these days). Even gel batteries (which I will never, ever buy again unless it's unavoidable) can manage this without any difficulty and they can continue doing so for longer periods - most deep cycle batteries these days can be drained to around 20% capacity unless it's a LiFePO4 which you can apparently use 100% of (I haven't tested this because I'm not wealthy enough to own one or experiment on it if I did).
Charge rates on deep cycles vary. Ordinary lead acid at about 20% of rated capacity, so a 100Ah can be charged at 20A per hour. Gels should be limited to 10% (amps) and <14.1V so that bubbles aren't formed on the surface of the plates. AGMs are much more tolerant allowing charge rates typically of C/3 (40A for a 120Ah battery) and up to C/2 for spiral wound ("military") batteries - 37.5A for my Optima D31A. This tolerance comes from the battery acid being held in a glass matt rather than as a gelatine-like substance between the plates.
Word of warning for experimenters: you can still cook an AGM. Grab a 50Ah AGM and throw 100A at it. The electrolyte will boil quickly, over-pressuring the battery causing it to vent. Most AGM batteries are "VRLA" - valve regulated lead acid - meaning they have pressure valves in their cases preventing any gas from escaping under a certain limit, which forces it to recombine thus retaining the original electrolyte for the life of the battery. Oh, if you DO experiment, don't smoke or have any naked flames or sparks near the battery. It vents hydrogen. And oxygen. A spark means major flames. Add a burning fireball to spraying battery acid and chunks of lead and you've not only got an expensive cleanup bill, but you could be badly hurt.