Yes, DirecTV DVR's can record two shows at a time. DirecTV's Dvr's also buffer both Tuners in HD for 90 minutes instead of Dish HD DVR's 60 minutes. If you choose to add MRV to your account then any and all DVR's on your account can share content. If you get a non DVR HD receiver and have MRV (Multiple Room Viewing) you can playback any DVR content on the NON DVR HD receiver.
you can get a AM21 which would give you OTA channels but the limit is still 2 tuners to record.
So you can record 2 satellite, 2 OTA or 1 of each at the same time.