Can I train for running races AND triathlons?

I would say it probably depends on what result you're looking for in your races.  If you want to compete for your age group or just really do well, you might want to consider just focusing on one.  

There are a number of people on this site who did a 1/2 IM in the summer and a fall marathon.  I don't know what they thought of their results, but I was "satisfied" with mine.  I'm a MOP to BOP'er, I think I could have done better, but if you ask most people who race they'd probably say the same thing.  

Bottom line, if you wanna do both, I say go for it.  Good luck.

Gary

IMHO, your goals are completely compatible. Find a good half IM training program with an early summer race in mind, THEN up your mileage for the fall marathon. You don't say where your training is now, but you'll at least have to up the running mileage to 20-25 MPW to complete the half mary in the half IM. You can do that, and build speed, on four days running per week if you focus on quality runs. I include a tempo run, an interval workout, a moderate distance, and a LSD in my running week.

I trained for Chicago Marathon and did a couple centuries, while simultaneously training for sprint tris in late summer, and didn't "kill myself" (much to the disappointment of some here).Tentatively I'm planning a halfIM in early April and the Flying Pig in early May.

No problem, as Bear points out. I trained all year for triathlons only, which naturally led to improved run times, both short and long. My key race was a half IM in July, which left me in good shape (mileage wise) to push up running distances for fall marathon season.

I say go for it!  My times have improved because of my tri cross training.

Evelyn

Make sure you build that mileage slowly.  No more than 10% a week.  Your long runs should be run at least 2 minutes slower than your planned race pace.  Speed work comes later in the training.  I used the Galloway training method.  Saved my knees (IT Band). 

Good Luck

Evelyn