Yes. Any number of halves of split cards can be any card type. It's just that instant and sorcery halves are easiest to implement without peoples' heads aching.
The first part of casting a spell is to put that spell on the stack. At the same time, you choose how many halves of a split card you want to cast. (Usually this is just one, but with fuse, it can be both.) Only the characteristics of the half or halves you chose to cast will exist on the stack. Then, when the spell resolves, it will resolve only to the effects of whatever characteristics it has, as normal.
Note that if at least one half is a permanent half, the rules will have to be modified slightly so as to allow the spell to enter the battlefield and become a permanent. This is because as the rules are currently written, a split card has the characteristics of both halves as long as it's anywhere but the stack.
This means that no, split cards do not have to be of the same type on both halves.
Private Mod Note
Rollback Post to RevisionRollBack
How to use card tags (please use them for everybody's sanity)
[c]Lightning Bolt[/c] -> Lightning Bolt
[c=Lightning Bolt]Apple Pie[/c] -> Apple Pie
Vowels-Only Format Minimum deck size: 60 Maximum number of identical cards: 4 Ban list: Cards whose English names begin with a consonant, Unglued and Unhinged cards, cards involving ante, Ancestral Recall