Colorado actually does sign some US routes along interstates, but...

(updated 9/7/2021)

Colorado is somewhat infamous for not signposting its US routes where they are concurrent with interstates.  This is more than just signage policy: CDoT route logs actually divide US routes into segments, and these segments are discontinuous in cases where the US route shares pavement with an interstate.  So in a sense, CDoT considers US routes to be non-existent wherever their implied route is on an interstate.  This notion has resulted in at least one very strange sign, shown here:

Sanderson, May 2017

That was taken looking west on I-270 at its interchange with I-25.  Straight ahead on the Boulder Turnpike is the east "beginning" of US 36... that is, assuming one disregards the 1300-mile segment of US 36 behind the camera.  ​(Incidentally, heading the opposite direction, there is a "Begin I-270" assembly, but it is not accompanied with an "End US 36" sign.)

However, there are a few exceptions... that is, a few places where US routes are still signposted along interstates.  For example, US 160 is well-signed along I-25 between Trinidad and Walsenburg.  Both US 50 and even Business 50 are signed where they overlap I-25 in Pueblo.  ​US 24 is signed along the short segment it shares with I-25 in Colorado Springs:

NB I-25, near Trinidad

NB I-25, Pueblo

NB I-25, Pueblo

NB I-25, CO Springs

Also, in Denver, the segment of I-70 between I-25 and Vasquez Boulevard was triple-signed with US 6 and US 85 shields.  (Which was kind of a cruel joke, because there were no signs instructing drivers following those routes to get on I-70 in the first place!)  Since that portion of I-70 was torn down in 2021, I documented the condition of the signs before they were removed.  (I would be very surprised if US 6 and US 85 were still co-signed along the new I-70 after it is rebuilt.)  Heading westbound on I-70, the first such sign assembly was shown in this photo:

Sanderson, May 2017

That was posted about one block east of the Steele Street overpass, so I-70 drivers at that point were technically not on US 6-85 yet.  The semi visible behind the sign assembly was following the implied route of US 6-85, so obviously the driver would never have seen the signage shown there.  The first confirming assembly* that was actually visible to US 6-85 traffic was about a half-mile further ahead (*conundrum: can it still be referred to as a "confirming assembly" even if there were no signs directing traffic to turn onto the freeway?)  This was posted just before the York Street overpass:

Sanderson, May 2017

The US 6 and US 85 shields were twisted so far that they were really not even visible to drivers (except maybe those who happen to look out their passenger-side window when they are essentially right next to the signpost).  Google Street View images reveal that this assembly became deformed sometime between Aug. 2015 and Sep. 2016.

One more triple-sign assembly was posted ahead (although these two US route shields were liberated by 2018).  This one was right at the Brighton Boulevard overpass:

Sanderson, May 2017

Oops, that actually should have been "South" US 85.  I am told those were 1961-spec US shields, so it is possible that they dated back to the time when US 6-85 traffic was first directed onto this road.

So although CDoT does co-sign US routes with interstates in a few cases, they are certainly neither consistent nor meticulous about it.  Heading the opposite direction (east on I-70), there was only one triple-sign assembly, posted just past the York-Josephine off ramp:

Sanderson, May 2017

The upcoming interchange is where US 6-85 traffic exits and heads north on Steele to Vasquez.  But again: neither US 6 traffic (heading east on the 6th Avenue Freeway) nor US 85 traffic (heading north on Santa Fe Drive) is instructed to head north on I-25 and then east on I-70 to reach this point, so these assemblies were kind of pointless.  

Historically, CDoT did a much better job of co-signing US routes along interstates:

Summa, 1979

Lindsay, 1970

Summa, 1979

Research and/or photo credits: Jim Lindsay; Dale Sanderson; Michael Summa