You're describing a classic one-to-many relationship, here, and this is typically done by using a Main Form (based on the Invoice Table) and a Subform (based on the Invoice Items Table).
The Main Form will be in Single View, the Subform in Datasheet View.
After creating both Forms, go into Design View for the Main Form and add a Subform Control. When prompted by the Wizard, select the Invoice Items Form as the base for the Subform. If the Invoice Number Field is named the same in each Table, Access will automatically link the Main Form/Subform using this Field, and when you go into the Subform, the Invoice Number will automatically be populated.
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The problem with making anything foolproof...is that fools are so darn ingenious!
All posts/responses based on Access 2003/2007