Layering multiple network encryption protocols does not particularly improve the confidentiality or integrity of the payload data you are transmitting. While SSL is broken (the SSL2 and SSL3 protocols), TLS is considered relatively strong, particularly TLS1.2 and the upcoming TLS1.3. The same is true with SSH2 (virtually all modern SSH connections use SSH2), which also uses strong and secure algorithms. Layering multiple protocols increases the risk that one of the protocol implementations will be vulnerable to a fatal attack, making it potentially worse to layer them.
Fundamentally, all these different protocols are implementations of the exact same (or equivalent) algorithms. Both TLS and SSH use DHE or ECDHE to securely exchange a secret key, they both support strong ciphers like AES to encrypt your data with said secret key, and they both use strong techniques such as HMAC to protect the integrity of the data. They only differ in what they are optimized for. For example SSH has features that reduce latency for sending keystrokes, whereas TLS has extensive features to support a trusted PKI (Public Key Infrastructure).
Instead, what you should do is pick a single protocol that is well suited for your needs and use it. For something like a MySQL database connection, it would probably be best to use TLS. It is optimized for these kinds of connections whereas SSH has different optimizations that may not be necessary. In terms of the actual encryption algorithms being used, they are all equally strong.