Can I have two different types of water heater in the same house?
Three Phase Eel's comment is valid.  Look at redoing the whole system.  If you have natural gas in your area look at hooking up to it.  

The rest of this is off topic to your original question, but I think relates enough to TPE's comment to be worth posting.  

Gotchas:  Heating units were often oversized for the building.  My contractor sold me a 90,000 BTU/hr boiler that rarely runs more than 2 minutes in 15 even in mid winter.  I have since realized that I could heat my house with a demand water heater.

Sanity check for boiler operation:


Measure it's current duty cycle.  This takes a lot of patience, or you can put something like a kill-a-watt meter on it.  Usually heating appliaces are hard wired, so you would have to modify it to use a plug for the Kill-a-watt.
(If you find that it draws 300 watts for the blower, then it uses .3 kWh per hour of operation.  If it uses 1.2 kWh per day, then it it ran 3 hours.  3/24 = 12.5% duty cycle)
Now find the difference between the temp you want inside (70), and the average temp outside this week.  Suppose that is 25 degrees.
Look up what your coldest expected temp in winter is.  Easiest way is to look up your plant hardiness zone, then look up the temperature definition for that zone.  Suppose it's zone 3 which once in 10 years gets -40.
Currently it takes a 12.5% duty cycle to keep your house 25 degrees warmer than outside.
In your worst reasonable winter it's 70 - -40 = 110 = 4.4 times your current difference.  So your present unit should have been running 4.4 times 3 hours or 13.2 hours on the worst weather you are likely to have.  


That would mean that your previous unit was oversized by almost a factor of 2.



It's probably worse than that.  In cold weather we are better about closing doors and windows.

So by doing this you can 'right size' your replacement unit.



This still is a terrible way to do things, as even if you size it perfectly to your worst case, it's underused most of the time.  The best system I've seen for this was a school that had 5 small gas boilers.  Each was about 200,000 BTU/hr.  Each one had an 'on' point 2 degrees differerent.  So one boiler would turn on at a temp of 140F and off at 150.  The next would turn on at 138 and turn off at 152.  The third would be at 136 and 154.  During most of the year boilers 2 and 3 would sit there.  #1 would carry the load.  

The other two were set up similarly for domestic hot water, but at lower temps.  

They were also set up on quick connects.  If we had trouble with a unit, we could disconnect it in about 10 minutes, put it in a pickup, drive it to town, and they could fix it, without our paying $120/hour for their time driving.