I wish I had more time to test this, but I am confident this is a limitation of the system. The assembly moduel is simple by nature.
The setup as I would see it, would be that;
Item A and Item B, are "Assembled to Stock".
Item A and Item B are set as planning lines on a job with the usage link code ticked. Type = Billable/Budget
An Assembly order is created and posted for the construction of item A and B.
Item A and B, are posted as Job Journals. (this will consume the Items against the Job).
The Sales Invoice for the Job is then created.
Hope this helps. (But it sounds like when the Sales Invoice is created in your scenario for Item A and B, there is no associated Assmebly order created in the back ground, where the Sales Invocie is created from a Job).