Enabling either Smart guides or the Snap to Point command will allow you to snap anchor points from one path to the anchor points of another path, even if the two paths are on separate layers.
If you're going to join two separate paths together into one single connected path that can be done using multiple methods. After the anchor points are snapped into the desired position the Pathfinder Unite command can be used to weld the two paths together. The paths can also be manually edited using the Scissors Tool to cut open the paths where they're butted together. The line segments that aren't needed can be deleted. Then the Join command (Ctrl/Command+J) can be used to connect the overall path.
Either method will result in the new, larger path being positioned on a single layer.