1. Spell clashing. When two different conflicting spell types are used, the magnitude of the spell gets reduced. EG you cast a 60 damage fire spell and a 30 frost spell. The lesser spell then reduces the primary (higher magnitude) spell by a percentage, formula, or direct value. The primary spell's side effect is dominant, and so deals the previously mentioned burning damage.
2. Spell diminishing. You cast the same 60 damage fire spell and a 30 damage frost. The total spell damage for the initial cast is 90 damage, but the primary effect (burning in this case) is reduced in length/magnitude in accordance to the magnitude of the frost spell or canceled out altogether..
This would allow casting different spells to be possible without becoming overpowered, but with some sort of drawback for using two different types. If significantly underpowered through these penalties, you could integrate a method of ignored resistance. For example when dual casting frost and fire on a target that has a resistance (for this case we'll say fire), he'll be unable to reduce/ignore the fire damage due to being affected by frost and fire simultaneously.
There's obviously other ways to handle this, but I feel this method would be balanced so as to not draw too much attention to casting spells.