I'm not really sure what you mean, GBIC is a type of interface convertor  and usually has SC Fibre connectors, the mini-GBIC you are referring to may be an SFP which is a smaller type of interface convertor and usually has LC Fibre connectors.

GBICs and SFPs will work together as long as they are the same type ie Single Mode or Multi Mode and you also need to make sure the TX and RX Optical Power levels are within the specified limits at both ends of the link.

On some switches the command "show inventory" may show the type of interface convertor installed.

SITE-A-CAT#show inventory
NAME: "SITE-A-CAT", DESCR: "Cisco Catalyst c2950 switch with 24 10/100 BaseTX ports and 2 GBIC (Gigabit Interface Converter) slots"
PID: WS-C2950G-24-EI   , VID: L0 , SN: FCZ1041Y0KJ

NAME: "GigabitEthernet0/1", DESCR: "longwave fiber gigabit ethernet port adapter"
PID: GBIC_LX           , VID: 30 30 30 30, SN: AGS094801V1

Or try the command "show interfaces gi/x/x/x capabilities" (where gix/x/x) is the interface number.

PE-CAT-A#show interfaces gi1/1/1 capabilities

GigabitEthernet1/1/1

  Model:                 ME-C3750-24TE

  Type:                  1000BaseLX SFP

  Speed:                 1000

  Duplex:                full

  Trunk encap. type:     802.1Q

  Trunk mode:            on,off,desirable,nonegotiate

  Channel:               yes

  Broadcast suppression: percentage(0-100)

  Flowcontrol:           rx-(off,on,desired),tx-(none)

  Fast Start:            yes

  QoS scheduling:        rx-(not configurable on per port basis),tx-(4q2t)

  CoS rewrite:           yes

  ToS rewrite:           yes

  UDLD:                  yes

  Inline power:          no

  SPAN:                  source/destination

  PortSecure:            yes

  Dot1x:                 yes

Hope this helps