Not just in the handshake, TLS moves these things called TLSPlaintext records (about 16kbytes each), not only in the handshake, but also for all the actual data - and they'll always have integrity protection to ensure bad guys can't change anything. TLS can't know the difference between a bad guy tampering with data and your crappy Internet mangling the data in transit, in either case the TLS protocol design says to "alert" bad_record_mac which your browser or similar software will probably treat as a failed connection, even if it happens mid-way through an HTTP transaction.
Because TLS guarantees integrity even if your fiber is a complete shit show, any TLSPlaintext records which do get from one end to the other are guaranteed to be as intended.