This is actually more of a complicated subject than you might imagine, but the short answer is no, you would most likely not want to combine seperate, broadband antennas of different make/model onto the same feedline.
Here's some excellent info concerning stacking/Combining antennas, which explains why what you want to do is not a good idea :
While it is possible to stack antennas for increased gain/directivity, it is very tricky and each antenna hooked together has to be exactly the same "model" and aimed in the same direction. Spacing and proper mounting/connections/phasing/etc. are key, and stacking is usually most beneifical over just a narrow range of frequencies.
Here's a good article on stacking antennas:
There are also a few excellent threads concerning combining or stacking antennas that go into much more detail, and provide much better info than I am attempting here, but I don't have the links handy, perhaps someone else has them available ...
The above links do a better job than I can of explaining things, but here are a few points :
You CAN combine seperate VHF and UHF antennas together with a VHF/UHF combiner or by using seperate VHF/UHF inputs on a preamp/etc.
Something which you could do with your antennas that might be useful would be to use seperate feedlines for each antenna with a A/B switch near receiver to aim different antennas in different directions w/o needing a rotor.
However, Even with the antennas on seperate feedlines, spacing the antennas on the mast is important as well, If the antennas are too close together, one can affect the other(and not in a good way). 1 wavelentgh spacing for the lowest frequency you will be using/your antenna is designed for is best, however in many instances you can get away with spacing them closer together than that ... More info on this in the first link I provided above ...
Another thing that is possible is, you can combine antennas onto the same feedline using a CM Jointenna(if you can still get these, I've heard of them here on AVSforum, but I've never used one), which allows you to aim, and use one of your antennas for one, specific channel.
The main problem with what you are wanting to do is that the results would likely be very, very unpredictable, and it's quite likely that one antenna will "cancel out" the performance of the other antenna on at least certian frequencies/etc, and increase problems such as multipath/etc.
In other words, one antenna is likely to affect the other one in a delitirous manner, and you'll end up with something which will "operate" in a very unpredicatable manner(much like what we call a "random wire antenna"), instead of as the directional, hi-gain antenna which your antennas as used seperately would be.
Some folks do seem to have some luck occasionally with this sort of thing though, and can effectively use one antenna to help "phase out" interference problems, or at least some of the signal from a strong, unwanted local station in order to receive a station well on an adjacent channel -- But, again, it might work well for one channel(unpredicatably), but work horribly on another desired frequency/station you wish to receive.