Pattern cutting question (interfacing)

I started sewing about a year ago, and only make handbags/totebag types of items.

My pattern cutting skills probably leave a lot to be desired, but I find that when I cut interfacing and the fabric pieces separately, they are invariably slightly different.  I've tried layering the interfacing under the fabric, but I'm not happy with those results either.  Lately I've been ironing on the interfacing before I cut, and then cutting both together.   I'm curious what more experienced sewers do?  I mostly use a rotary cutter.

Also, patterns that require cutting on the fold seem to give me fits.  Even after trying to iron a crisp fold on the fabric, I never get it laid out exact enough for my liking, and I can't layer two folds on top of each other to cut out both sides at once...they always shift.  What I've started doing is making a copy of the pattern, full size (not to be cut on the fold), and then cutting out my pieces that way. Then I can easily cut out two sides of a bag at once.  Does anyone else do this, or have tips for cutting on the fold?

Thanks!
Cindy

I do everything you've described (fuse interfacing before cutting, make pattern pieces that don't have to be cut on the fold, and use rotary cutting supplies for bags). 

I also like to use freezer paper to make my pattern pieces.  Freezer paper has a waxy backing that adheres to fabric when ironed on, but it can be peeled off easily when you're through cutting.  For me, it's way quicker and more accurate than using pins.  The freezer paper pieces are only good for maybe 10 - 15 uses but, unless you're mass producing something, they work out nicely.

I love freezer paper as well.  I use it for all my sewing including patterns I draw-up myself as well as store-bought ones.  It's easier, more accurate and quicker.
I wouldn't stress about the interfacing vs fabric pattern cut-outs.  Mine are usually off a little as well and I always trim the interfacing to match the fabric after ironing them together.  (Ironing the two together and then cutting out the pattern would be too much of a waste for me.)  I haven't had problems with things lining up while sewing everything together.  I have found that sewing is alot more forgiving than you think. 
If things are shifting too much, take time and use more pins.  Constantly check your alignment and be sure everything is flat on the same surface.  I have a short rug in my living room which has hardwood floors.  If I try to lay out my fabric and pin something that's partway on my rug and wood floor, it never works out.  I make my lazy self walk into the kitchen (literally 3 steps away) and pin it on the large flat floor with no rugs or chairs in the way.  It always turns out better.  You might also consider pinning your fabric together on the fold first, then laying your pattern on top and then pinning again.  Good luck.

I have tried several different ways and the best way that works for me is to do them separately. When I am cutting a fabric on the fold I iron it and then I line it up to the edge and pin it, then smooth it out to the corner, hold it in place and pin it. I do the same for the interfacing (without the ironing part) and it seems to work pretty well for me. If I am cutting out a pattern even if it is square I find that cutting out with scissors in much easier for me than a rotary. This is just what works for me, I hope this helps. Happy sewing!