A question about cleric’s alignement restriction on spells

A Cleric can only cast spells of the same alignment to his own or his deity’s.

What happens when a character multiclasses into another spellcasting class? Does the Cleric’s alignment restriction extends to those spells learned with an arcane casting class?

For example: Is it possible for a wizard to cast a spell with the Chaotic descriptor if he/she has multiclassed into a cleric whose deity is lawfully aligned?