relationship between Parliament and the Restoration monarchs, Charles II and James II, change following the English Civil War?

After the Glorious Revolution, the Restoration Monarchy was demolished and was changed to Constitutional Monarchy. This happened after King James II fled the throne and the Parliament decreed a vacancy over it. The Parliament had offered King William and Mary (daughter of King James II) as co-regents of the throne. They were able to establish the English Bill of Right and restore Roman Catholicism all over England.