Actually, there is a "fourth" type of conditional sentence called "Mixed Conditionals."
YES, you can put together in one sentence type 2 and type 3 conditionals to express an unreal past with results in the present.
If George had attended the meeting (last week), he would be aware of the latest developments (now).
If costs hadn't gone up twenty percent, we would be making a profit.
If you had received the press release, you would know about the product.
For more details, you can check "The Oxford Dictionary of English Grammar." (Conditional, p. 84)