C172 VFR inbound to LVN described a confusing clearance and/or lack of same when first exiting Class B and then routed back in without a Class B clearance; the reporter alleging ambiguity in the way ATC handled the flight.

Narrative

On a dual instruction VFR cross-country training flight to LVN; I was the CFII monitoring and providing dual instruction to a private pilot conducting cross-country training in preparation for an instrument rating. Upon establishing communication with Minneapolis Approach approximately 5 NM northwest of CFE; we were cleared into the Minneapolis Class B airspace on our direct routing with instructions to maintain VFR at or below 4;500 MSL. As we crossed CFE and continued southeast-bound; the Controller issued us a vector for MSP arrival traffic; instructing us to fly heading 170 and descend to maintain VFR at or below 3;500 MSP. Our compliance with this ATC instruction placed us below the floor of the Class B airspace in the area. Upon continuing on the VFR heading for 5-7 NM; we were instructed to 'resume own navigation direct LVN'. At this point; the aircraft was operating under the floor of the Class B; which was at 4;000 MSL. Upon examining the new direct track to LVN from this point; the student and I both observed that the new direct routing would take us through the 3;000 MSL shelf of the Class B. I thus requested Approach to verify that we were cleared to transition the 3;000 MSL shelf; believing that descending below the Class B automatically voided our Class B clearance. The Controller seemed surprised by my request for this clarification; and responded in a slightly dismissive tone that we were 'cleared into Class B airspace'. We continued without incident; reported LVN in sight; and landed full stop. I believe there exists a certain ambiguity in the manner the Controller handled our altitude assignments while we were under RADAR control within the MSP Class B airspace. We were not notified of leaving the Class B even through we were instructed to descend below the associated shelf floor in our area. I suspect that the Controller's surprise at my request for clarification stemmed from having the assumption that his initial Class B clearance was still valid. If an aircraft is instructed by a Controller to descend below a Class B airspace floor; I believe more clarification should be placed upon informing the pilot(s) if re-entry into the Class B is approved should further ATC instructions place the aircraft in a position to re-enter the airspace.