The difference between intervene and interfere is that intervene is a situation in which usually describes someone entering into a conflict on behalf of a person or for the purpose of solving the conflict for both parties.
For example a teacher may intervene in a fight on school grounds.
Interfere would be used in a variety of situations wherein a group or person is altering or attempting to alter something for any number of reasons for personal reasons.
Interfering has an aggressive connotation, and intervening has a peaceful connotation (also used when intervention is necessary).
Note: These words can be interchangeable depending upon your bias or opinion.
Drug addiction intervention.
There was radio interference on my favorite radio station.