This is possible to run the two address-families under the same OSPF process since Cisco IOS Software Release 15.1(3)S.

You can do this as :
R9(config)# ipv6 unicast-routing
R9(config)# ipv6 cef


Then :

R9(config)# router ospfv3 1
R9(config-router)#address-family ipv4 unicast
R9(config-router-af)#router-id 10.1.9.9
R9(config-router-af)#redistribute connected
R9(config-router-af)#exit-a


And then configure the OSPF link by means of configuration on the interface :
R9(config-router-af)#int ser 3/0
R9(config-if)#ospfv3 1 ipv4 area 236
*May 13 20:31:14.956: %OSPFv3-5-ADJCHG: Process 1, IPv4, Nbr 10.1.6.6 on Serial3/0 from LOADING to FULL, Loading Done
R9(config-if)#ospfv3 1 ipv6 area 236
R9(config-if)#


This is where I think it is really powerful.
I recommend you to check IPv6 and OSPF only with the keyword “ospfv3” such as :

R9#show ospfv3 neighbor

          OSPFv3 1 address-family ipv4 (router-id 10.1.9.9)

Neighbor ID     Pri   State           Dead Time   Interface ID    Interface
10.1.6.6          0   FULL/  -        00:00:33    15              Serial3/0

          OSPFv3 1 address-family ipv6 (router-id 20.1.9.9)

Neighbor ID     Pri   State           Dead Time   Interface ID    Interface
10.1.6.6          0   FULL/  -        00:00:31    15              Serial3/0
R9#

On R6 we can see now :

6#show ip route ospf?
Hostname or A.B.C.D  ospf  ospfv3

R6#show ip route ospfv3
Codes: L - local, C - connected, S - static, R - RIP, M - mobile, B - BGP
       D - EIGRP, EX - EIGRP external, O - OSPF, IA - OSPF inter area
       N1 - OSPF NSSA external type 1, N2 - OSPF NSSA external type 2
       E1 - OSPF external type 1, E2 - OSPF external type 2
       i - IS-IS, su - IS-IS summary, L1 - IS-IS level-1, L2 - IS-IS level-2
       ia - IS-IS inter area, * - candidate default, U - per-user static route
       o - ODR, P - periodic downloaded static route, H - NHRP, l - LISP
       a - application route
       + - replicated route, % - next hop override

Gateway of last resort is not set

      10.0.0.0/8 is variably subnetted, 11 subnets, 2 masks
O E2     10.1.9.9/32 [110/20] via 10.1.69.9, 00:04:16, Serial3/0
      20.0.0.0/32 is subnetted, 2 subnets
O E2     20.1.9.9 [110/20] via 10.1.69.9, 00:04:16, Serial3/0
R6#