QB does not handle landed costs, so you have to use a work around
on the original purchase, add a portion of the shipping to each item total.
On the bill, select the item, enter the qty received, and click over to total amount and enter the item cost + a portion of the shipping, when you click out of the total cost block QB will do the per item rate.
When you get third party shipping, pay the bill using a clearing expense or asset account (it makes no difference which kind of clearing account you set up in teh chart of accounts).
then edit the original bill
for each item, increase the item total cost by a portion of the third party shipping
then use the accounts section at the top, select the clearing account, and enter the full amount as a negative number
save and click though any warnings you get about payments being applied
QB will redo the purchase cost per item as of the date of the bill, and if any item have been sold in the interim, QB will make COGS adjustments resulting from the increased per item cost.