The problems with multiple inheritance have been the reasons to forbid it and enforce the usage of interfaces, as java has been designed. Since many real-world use cases of multiple inheritance are solvable with interfaces without the problems of MI.
If you search the net, you will be presented with examples, where multiple inheritance is called the only real solution. It seems possible to write programs without it, as you can see in java-solutions.
At least in those cases where it really is about implementing an interface I would suggest implementing an interface.
Implementing multiple interfaces is free of those problems, because it is only a contract what data / methods you have to provide, and not how.
So interface is about contracts, and inheritance is about common data and methods.