Reddit mentions of Mathematical Biology: I. An Introduction (Interdisciplinary Applied Mathematics (17)) (Pt. 1)

I have James D Murray's Mathematical Biology which is quite good (although I must confess I haven't read all of it) but perhaps out of the scope of what you'd be looking for.

I've looked up the recommended reading in a mathematics module for a biology degree at my university and they recommend Paul Monk's Maths for Chemistry: A chemist's toolkit of calculations so perhaps that might be useful for you (although it seems from the title it would be more geared towards chemists, yet that's what they reccomend).

The classic text is J.D. Murray's Mathematical Biology, but the last time I looked at it, it was a little long in the tooth. Maybe the second volume picks up a bit. No matter, look at it if you want to get a clear understanding of the background and classic problems.

There is a great deal of focus on computational molecular biology lately (networks, DNA computation, molecular programming, etc). Some of the people on the forefront of these fields include Niles Pierce, Erik Winfree and Drew Endy. Check out their papers and you'll get answers to many of your questions. On Winfree's page there is a whole list of collaborators which will keep you busy for a while.

The applied math degree will help, but if you really want to do well you'll need to learn a ton of biology. And I mean really learn it, there is nothing worse than a mathematician coming in and doing some cheap models of a biological system and claim that he has found a novel result when in fact it has no bearing on the underlying biology.

I would recommend checking out later sections of this book http://www.amazon.com/Mathematical-Biology-Introduction-Interdisciplinary-Mathematics/dp/0387952233 (I can PM you a pdf if you want it). It goes into protein-protein bonding and protein-small molecule reactions in glorious mathematical sparseness, succinctly covers molecular biology/bioinformatic screens, and of course covers everyone's favorite intro PDE- the predator prey model; even after taking upper level undergraduate biochem/molecular biology courses seeing it all put so succinctly was a real treasure. Some of the math is relatively advanced for a developmental math course, but given that all of your biology/chemistry majors should have covered this material before (sans math in most cases) it shouldn't be too hard for them to jump into.