You could export the private keys from bc.i and import them into multibit classic (HD does not allow you to import private keys), but its not a good idea to do so. For one you risk exposing the private keys while doing so and lose all your coins in the process. Secondly you would need to do this on a regular basis as each wallet will create new addresses the other does not know about. Thus keeping the wallets in sync is tedious. It might also confuse bc.i or multibit when you create a TX with one that the other does not know about and might even cause issues with the transactions you create e.g. if you use the same input on two different transactions because the wallets were out of sync.
May I ask why you want this? Maybe there is another solution.
What do you recommend me to do?
Use both. Keep the larger amounts on your computer by sending them to your multibit (or better multibit HD) wallet from time to time and keep the change on bc.i.