We are assuming that you are talking about TWO 12 volt batteries. People call dual purpose batteries and GC2 6 volts deep cycle so we need to know what you have. Since you said parallel our best assumption is 12 volt batteries but you did say DEEP so people could also think 6 volt. Do you have 12 volt or 6 volt batteries?
Solar and inverter dont matter. As Grit said, BUT be sure to connect system positive and negative in a balanced manner. Don't connect the rigs positive and negative to one battery, you want the positive to one battery and you want the negative over to the other side of the other battery.
Your solar is then going to charge both batteries the same way any other charger would be interacting with the batteries.
This pic is from the website "12 volt side of life". IF your batteries are 12 volt batteries they would look like the black ones on the left. They are showing you how to do basic wiring of both 12 volt and 6 volt batteries. If you have TRUE deep cycle 6 volts then you are actually asking about a series connection like the red batteries on the right.
