Are Arcane Arcane Tricksters still limited to Enchantment/Illusion spell schools when multiclassing with a Wizard At higher levels?

Please help me with Arcane Trickster Wizard multiclass spell options?

I have a Rogue-Arcane Trickster Lvl 10, Wizard-Bladesinger Lvl 6. I understand they use the other spell slot chart in the multiclassing section of the PHB. Now I know Arcane Trickster can only select Enchantment and Illusion spells. I also know you can add all spell schools in a Wizard’s Spell book.

Are Arcane Arcane Tricksters still limited to Enchantment/Illusion spell schools when multiclassing with a Wizard as they gain more levels in Arcane Trickster?