。
The parents' joy was immense.
Literal
Parents [possessive-の] joy-manner [topic-は] very great was.
喜びよう uses the suffix ~よう (manner/way of doing) — 'the way they were happy' or 'the extent of their joy.' This ~よう nominalizes the emotion as a visible display. とても大きかった (was very great) describes the magnitude.