When an AFCI or GFCI breaker is tripped or turned off does it break the neutral line also?
GFCI's must break neutral
GFCIs (of all types) are required to break hot and neutral, unlike regular fuses, switches, or breakers.  This is not spelled out in UL 943, but is implied by the requirement in UL 943 6.7.2.2 that a GFCI must still trip and disconnect the load circuit from power if the line-hot and line-neutral connections are interchanged.
Some AFCIs also break neutral, although they are not always required to
Because early AFCI designs were derived from GFCIs, they inherited the property of breaking the neutral (as well as being sensitive to gross ground faults).  However, some more modern designs (Mod 3 THQL AFCIs, most notably) dispense with the ground-fault detection, and thus may or may not break the neutral wire.  (As to the standards: UL 1699 13.3 requires receptacle-type AFCIs to break neutral, whereas circuit-breaker/loadcenter-type AFCIs have the option to not do so.)