This is a fully taxable transaction where the "proceeds" of the sale is the combination of the cash plus the fair market value of the stock received. It's "as if" you received all your proceeds in cash and then took some of that cash and bought some BAT stock.
Tom Young
NOTE TO FUTURE READERS OF THIS ANSWER:
You must understand that the answer given is relevant to this particular transaction. There simply is no one or two sentence answer that covers all cash + stock mergers/acquisitions.