I've just found three sets of mixed trains listed as such in the Delaware & Hudson's public passenger train timetable effective September 25, 1938.
The pair between Fort Edward and Lake George via Glens Falls had the shortest runs by far: just 14.5 miles each way. Train 161 left Fort Edward at 9:05 a.m., arriving at Lake George at 9:50. As Train 162, it left Lake George at 10.00 a.m., arriving at Fort Edward at 10:40. Obviously, the railroad didn't expect it to do much switching at Lake George! These trains were scheduled to allow passengers to make connections to and from Albany and New York on main line trains.
The trains on the Adirondack Branch traveled 57.1 miles each way. Train 181 was due out of Saratoga Springs at 8:40 a.m. -- twenty minutes after #1 from New York and Albany had arrived. After six intermediate stops it was scheduled into North Creek at 11:40 a.m. Train 182 left North Creek at 1:25 p.m., reaching Saratoga Springs at 4:20, in time for travelers to transfer to a southbound local from Whitehall to Albany, connecting to New York.
One mixed train each day also served the former Chateaugay Railroad, 83 miles each way. Train 82 departed Plattsburgh at 6:40 a.m., making up to ten stops before arriving in Lake Placid at 10:50. The return train, #81, left an hour later , arriving at Plattsburgh at 4:15. A traveler from New York (perhaps bound, with a guard, for the state prison at Dannemora) could catch the mixed at Plattsburgh, but anyone arriving inn Plattsburgh at 4:15 p.m. would have had a very long wait for a southbound, since none was supposed to arrive until 10:42 p.m.
Finally, southbound #!8 was carded as a mixed train for its 113.3 mile run from Rouses Point to Whitehall, leaving at 7:05, making up to 14 intermediate stops and arriving at 2:20, allowing travelers to catch the Laurentian at 2:25 or an all-stops local at 3:20. It would be interesting to figure out whether this train collected milk cans and/or milk tank cars. There is no northbound train on the main line listed as mixed.