This is not a complex subject but it can be tedious to describe. You need to look at your files to see if they are truly interlaced or not. Right click on a raw one in Windows and look at the details. If it states under Frame Rate "24", then your original files are not interlaced. However, it may say 59 or 30, which is an indication they are.
If your files are truly 24 (or 23 FPS) then you can set the Vegas timeline to HD1080-24p, and match the data rate. BTW Vegas does this automatically on your first clip dropped onto the timeline if set this way. Then let Vegas convert it to 60p under "Render As".
However, if for some reason your project is truly native interlaced footage then try some of these tricks. And there are tricks to approach de-interlacing. It depends on the desired quality of your final output.
1) You could output the product into a native Interlaced = "equal" setting in Render As and then convert it in Handbrake to 30 or 60p FLV or with Adobe Media Converter if available. This seems top produce good results.
2) Let Vegas Pro do the conversion for you under "Render As" AVC Main Concept Internet 30p. Or AVCHD-60-i then let the internet convert it automatically.
Some people convert there footage before editing (transcoding). Some do it internally in Vegas and some use an external program like Handbrake, Adobe Media Encoder or Sorenson Squeeze.

Good luck.
Jim