Do IFR / VFR weather minimums include ceilings?
The FAA does not define &quot;LIFR&quot; or &quot;MVFR&quot;
These are not terms that the FAA makes reference to.  Go look in the FAR/AIM, section 1.2.  You'll find VFR defined, and IFR defined, but not the other two.  Why is that?
Because those are terms used by the National Weather Service, not the FAA
That means that if you want to operate an aircraft, you obey the FAA weather minumums that are provided in your second link.
The information in the first link is about reading weather reports.  As far as the FAA is concerned:

VFR is VFR
MVFR is also VFR
IFR is IFR
LIFR is also IFR

So answer my question
Ok.  If you're departing from an airport, and you will be in class B airspace from the moment your wheels leave the ground, then as long as you have 3 miles visibility and you don't touch a cloud you can fly.
However, it's not likely that you'll be in class B airspace from the moment you leave the ground unless you're departing from the main airport (LAX, ORD, and so on) and if that's the case odds are you're on an instrument flight plan anyway.