Can I have public and private IPs on my LAN interface
This can be accomplished by defining an IP alias VIP for the additional subnet on the internal interface, and adjusting firewall rules and outbound NAT accordingly. DHCP cannot be provided to both subnets from pools on the same layer 2 network.
Note that while this is technically possible, it is not recommended for security reasons. It is generally a bad idea to mix public and private traffic on the same segment if it can be avoided. It is best to define a separate interface for the public traffic to keep it isolated from the private network.