Train on road bike, race with a tri bike

You will want to get a mix or riding in, especially as you get closer to the race to make sure you are comfortable and adapted to the tri bike's position.  It is a bit different and things like neck and core strength come into play more when you are staying aero.

But you can certainly do most of your riding on the road bike.  That is also what I do.

Tri bike costs more than my road bike but not by much. I buy carbon bikes with ultegra parts on most of my bike other than my cross bike as it gets beat on pretty badly so they are all pretty comparable in price.

I ride road bike with my bike race team and when I race bikes. I now use my cross bike as my winter and crappy weather bike. Once it gets nice outside and roads are clear of salt, I ride my tri bike most all the time except with my bike race friends.

Of all my bikes my tri bike is most comfortable. I have carpal tunnel so in aero my hands are happy and find while riding any other bike in time my hands go to sleep.

Same here.

Especially when it come to group riding, a road bike is much safer when drafting.

With the race wheels on, the tri bike "costs" more.  Without it, they are pretty close.  But my road bike weighs 14.1 lbs. while my tri bike is closer to 20.

My road bike is well into the 20's while my tri bike is right at 20 lbs.  Both are a fraction of the weight that I still have to lose!

Yeah, but I bet your road bike doesn't weigh close to 204.1 fully loaded. 

I'm building a road bike for this reason, and to race road races starting this year.  I can't wait to post my first bike porn next week or so. . . .

I've had road bikes before as well as my tri bike and I always enjoyed group rides.  We don't have to worry about many killer hills here in Louisiana :-).  I had to get rid of the roadie and I missed it alot.  So, now that I was able to afford a new road bike build, I jumped on it.  Good luck!

Get many rides in on your tri bike to get the handling down...

I love/hate watching people on tri bikes... in the aero position... trying to go around cones and turn around points... with the inside pedal at the bottom... crash.

I spend the weekdays riding the road bike and the weekends riding the tri bike, that is because I usually ride a trail on the weekends so I don't have to worry too much about traffic and stopping for pedestrians and cars on my tri bike.

My road bike is less expensive than my tri bike. Road bike 20lbs and tri bike 21lbs.

I see no reason why you couldn't train on one kind of bike and race on the other kind but why bother? 

Maybe it's because I only have one bike (the tri bike), but I don't see any reason not to do all of my riding on the tri bike.  If doing a group ride, I just don't do aero.

I felt that I could live with one "superbike" at first (I have a Cervelo P2C 2008 as my only bike) but I'll now be the first to admit that if you right regularly with groups on weekends and most of those rides end up being mountain road rides (4000 feet of climbing is typical), you'll really, really wish you had a road bike with a compact crank as you gasp for breath just barely stopping from tipping over because of your superlow cadence. I'm the ONLY tribike on those rides, and only the strongest guys are still running TT-gearing (53/39 front, 12-25 back) - most others are on compacts or triples. Until I get the cash though, it's going to be more of a sufferfest with lowrpms with my TT bike on 12% inclines....

Interestingly, I haven't had any significant problems with the shifters being on the bar-ends versus the STI integrated road bike ones. I felt like an expert dancing around with multiple shifts all over the place on my aerobars within 1-2 rides, and I don't even notice the shift issues much anymore, especially now that I can ride with one hand on the horn and one hand on an aerobar to shift.