While not an interstate, the (very controversial) M3 Twyford Down section was included in South Downs National Park when that was created in the late 00s. In the early 90s when the road was built amid protests, it wasn't part of the 'Area of Outstanding Natural Beauty' that preceeded the park.
Likewise when they converted the New Forest from a sui generis entity dating back 900+ years to a National Park they expanded the area it covered, and rather than the M27 basically ending on the boundary (half the overbridge at junction 1 was in the area) a good couple of miles was suddenly inside the Park.