Router Details :
model number Cisco 2811
With switch model detail- NME-16ES-1G-P
once if you switch from router to switch its showing as
To download an image you need a valid Cisco contract which i think you have.
The EtherSwitch service modules support the same Cisco IOS Software images as the Catalyst 3750 and Catalyst 3750-E Series Switches
YOu can download the image to the router flash and then do an xmodem to transfer it to the ether switch module.
Have a look at the software section in the below link