In this area all highway passes are easy. You'd have to go out of your way to find something that would be a challenge or tight squeeze for your rig.
Banff is on the Trans Canada Hwy, which is divided hwy all the way through the park.
US93 becomes BC93 and enters Kootenay Nat Park at Radium. Before that it meets BC95, which would take you to US95 and CDA. If you want to make loop, consider taking BC3 east to Alberta (very easy pass), and AB22 north along the front range. 22 goes all the way to Hwy1, or you could turn west at Longview (this is Texas style oil country) and take Hwy 40 through AB parks to Canmore.
Sure you could also take 3 to 2 and north to Calgary. But unless you want to drive through the city, I don't know why you'd want to.
Another way in/out of the Nat Parks from BC is Hwy from Golden through Yoho NP to Lake Louise. BC95/93 from Golden south travels through the Rocky Mtn Trench, a broad valley that is the origin of both the Columbia River (which exits to the north) and the Kootenay River (flowing south to the USA).
Get yourself a book and official guide to the Canadian Rockies Nat Parks, and check what you want to see and do in that complex.
