My mage can cast the "improved identify" spell.

But it seems to only work on one handed items, since the spellbook becomes unavailable, when puttint a two handed weapon into the primary hand to identify it.

Any chance to identify those items?

Actually you can just place the two-handed item in off-hand slot and cast your spell with the mage book like always.

No, you're right as well. You need the spellbook in your mage's hand to open it. Once it has been opened, you can put it into your mage's inventory, put other objects into your mage's hands and still cast spells.