In D&D 3.5e, if I multiclass my wizard with a sorcerer, would I be able to spontaneously cast my spells like a sorcerer and still get the rest of the spells that a wizard gets? Or is that not possible?
Yes and No.
You get both sorcerer spells and wizard spells, but you must keep track of them separately. Your sorcerer spells must come from the limited spells you have chosen to learn as a sorcerer, have their save DC set with Charisma, and use your sorcerer spells per day. Your wizard spells must be prepared from a spellbook, have their DC set with Intelligence, and use your wizard spells per day.
The two do not mix, and you do not get the ability to spontaneously cast your wizard spells (or prepare your sorcerer spells from your spellbook).
But see the ultimate magus prestige class from Complete Mage for a way to partially mix the two, as well as advance both at the same time.