Typically when I work with structural framing I do one of two things (depending on sloped versus flat framing):

Flat framing is simple - make sure your boundaries are correct (walls, primary beams, etc.) and draw a beam system at the correct level. To modify the elevation of the beams, you will need to either adjust the level they are associated to, or adjust the elevation parameter of the system.

For sloped framing - I set my work plane to be the underside of the surface (such as a sloped roof) and proceed to draw the beam system. If you haven't set boundary members beforehand, you are going to want to do so prior to creating a beam system. You should notice that when the slope of that surface changes, the beam system (and associated members) will move with it.

For both situations make sure that when you draw the beam system, that the elevation of the system object is at 0 (unless of course you intend on using an offset) and that no other parameters are throwing your model off (like working off of an incorrect level).

Hopefully that helps a bit. If this is what you have been doing, then there might be a problem with the beam family that is being used within the beam system. Have you tried these methods with an OOTB beam family?

The flat framing is pretty simple.

You were right that there was something wrong with the log beam itself (will have to fix that). When I switched it to OOTB family then it was flush with the roof. I also used the log beam for the flat framing and it did the same thing, but I used the elevation parameters in properties to bring it up to where it needed to be. But for the sloped part the elevation parameters is gone - is that normal?

I could have sworn that the elevation parameter existed for sloped systems, but upon review (in RVT 2014) I did not have one. Strange. Not too sure about that one, sorry.

However, you should not need to rely on workarounds to fix this. Once you fix your beam family everything should work as intended! Check it to see if you have any modeled or annotative elements in the family that are above the beam sweep. Even if you have a visibility parameter on them, I recall that they will affect the top elevation of your object as long as they exist in the family at all.

I tried to find what could be causing the gap in the beam family, but I couldn't find anything. Maybe you could help? I've attached the family.
Thanks again.

I took a look at your family - you have a lot of unnecessary Reference Planes in there. Edit the extrusion and remove all those RP in a left/right view. Constrain the extrusion to the centerline/reference level RP outside of the "edit" function instead. This fixed the family for me.

That did it! Thank you. Didn't realize that having too much RP can change the family.