60A two pole breaker supplying a sub panel (220v) - how many amps for separate 110v legs?
Jeffrey is correct. You will have 60 amps of 240 volt power available.

As to the use of single pole breakers for a multiwire branch circuit, that is a code violation unless the breakers are tied together with a handle tie from the manufacturer. You can't use tie wire, a nail, or any other unapproved method. Better yet, you can use a common trip 2 pole breaker. This is the preferred method.

Informational Note: 110 and 220 volts are not normally available now. The voltages keep moving up. Most equipment is now rated for 125 and 250 and the National Electrical Code lists 120/240 or 120/208 as the nominal voltages for dwelling units.