Brett Kelver, Assistant Planner for the City of Milwaukie sent me this:
We have an opportunity to comment on and make corrections to a bicycle map that is being prepared as part of a larger, Metro-region SmartTrips program. The Portland Office of Transportation has sent us a draft version of the map and we have posted it on the TSP website for your review. Please take a look and send me an email with any comments or corrections by 5:00pm on Thursday, April 19th. A cursory glance shows that some of the parks are mis-identified, and you may see routes that are inaccurately labeled. Please let me know what you see that needs correcting, as this is a great chance for us to help develop a useful resource.

You can follow the link to the bicycle and pedestrian site

You can follow the link to their map.

(The map image is currently a little bit fuzzy—they will try to get a sharper image up on the web ASAP.)

Comments Update.
JC asks: Thanks for posting this. Do you happen to know if Main Street [right past ODOT] currently connects to the Springwater Trail or is that planned?

Yes, JC they do connect.  To get on the Springwater on the east side of McLoughlin… From Milwaukie center take Main St. North, past the old Southgate Theater, (where a Park & Ride is planned), until Main St ends at SE Moores St. Turn left up to McLoughlin Blvd, and get on the sidewalk there at the vacant bright yellow car dealership buildings. Head north along McLoughlin on the sidewalk about a block, but take some care as the walkway is littered with debris. (Maybe Portland or Milwaukie can clean this sometime?) The sidewalk takes you right to the beautiful bright orange Springwater bridge, and immediately after crossing under, the asphalt trail will take you up to the Springwater path. Again, take a little care on that path since theres a sharp turn and a steep dropoff.

And, you can also catch the path at about one block west of McLoughlin,  there is a short access path that puts you on the Corridor just west of the new Johnson Creek Springwater bridge.

Mapquest map.