What is a hybrid wallet?

A hybrid wallet allows you to send and receive Bitcoins just like any other wallet. However, the Bitcoin private key which is required to send money is encrypted in your browser before it reaches our servers.
Therefore our servers only hold encrypted private keys and neither we nor anyone else can spend your Bitcoins. Only you.

a good wallet should give us the option to control our private key (many of bitcoin wallet kept this out of our control, can be good.. but can also be bad) by having the private key, we can move the wallet to any wallet (even to QT wallet installed on our computer) but we need to keep the private key safe..
if you need a good bitcoin (BTC) and bitcoin cash (BCH) wallet, try strongcoin, i've been using it for more than 3 years and so far happy with their service, we can access our private key, and import or export private key, and even creating paper wallet..

https://strongcoin.com/?ref=1DiynNpCVxwx5vUyLwyzbkxJUn72KxjusQ

Give it a try