There's already a north-south bypass for I-35... SH-130. For those who are willing to use it, it's very effective at avoiding the mess that I-35 through Austin is. More than once, I've been able to travel from Georgetown to San Antonio and vice versa during peak hours without hitting any congestion. It costs almost $20 for toll-by-plate from I-10 to I-35 North, but well worth it for a long-distance trip. It's about 90 miles long, and has a speed limit of at least 80 mph, 85 mph south of SH-45.
SH-45 is a loop around the east side that utilizes a segment of SH-130.
US-183 between SH-71 and US-290 is currently being upgraded into a toll freeway with frontage roads, again built to interstate standards. That will form an "inner" loop utilizing I-35 near Downtown, SH-71, and US-290.
It's not interstate highway, but is toll freeway built to interstate standards.