Splitting Roads at intersection for ArcGIS Network Analyst?

The Feature To Line (Data Management) geoprocessing tool can be used for 'cleaning up' the data.

The help file mentions:

Where input lines or polygon boundaries touch, cross, or overlap each other at locations other than their start and end vertices, they will be split at those intersections; each of the split lines will become an output line feature. If an input line or polygon boundary is not intersected by another feature, its entire shape will still be written out as a line feature.

In Addition, remember to set the Preserve attributes option to true, in order to preserve the attributes in the output file.

You can use the Planarize Lines tool in ArcGIS (ArcEditor or ArcInfo license is required).

Keep in mind though that you would lose the overpass/underpass information in this case since all the intersecting lines will be splitted. More general reading on splitting lines is available here.

ET GeoWizards has a split Polyline with Layer tool that might work for you. It requires the polyline layer you want to split (creates a new shapefile or feature class) and a layer that it uses to split the lines. I used it to split pipes (polyline) into zones (polygon) and it worked nicely but it works with two polylines as well.

If all your roads are part of one shapefile/feature class you should be able to add it twice to your mxd and rename one. ie roads1 and roads2 and then use roads1 to be split and roads2 to define were the first is to be split. I haven't tried this so hopefully it works in practice as well as theory.