Virtualbox host only adapter interface doesn't get an IP
That is entirely normal.
A Host Only Adapter is isolated and does not include Internet. The Host Only machine should be able to communicate with the Physical Host Machine, and then would have an IP on the Host Machine.
Change the Host Only Adapter to NAT if you wish it to have Internet Access.
To avoid confusion, here is a decent article on connecting a Host Only VM to a Host machine
Connect a Host Only VM to Host
Create the Virtual Network First, you must set up a virtual network that the host-only adapter(s) will communicate through.
In the VirtualBox window, click File > Host Network Manager > Create. Check Enable under the DHCP Server column of the network you just created. Select your network and click Properties. In the Adapter Tab, select Configure Adapter Manually and use the following settings: IPv4 Address: 192.168.56.1 IPv4 Network Mask: 255.255.255.0
In the DHCP Server Tab, make sure that Enable Server box is checked, and use the following settings: Server Address: 192.168.56.100 Server Mask: 255.255.255.0 Lower Address Bound: 192.168.56.3 Upper Address Bound: 192.168.56.254
Click Apply and then Close Add a Host-Only Adapter to the Guest Machine For each guest you want to communicate with using the network from the previous step, you need to add a host-only adapter.
Select the appropriate guest machine Click Settings > Network Under the Adapter 2 tab, input the following settings: Enable Network Adapter: Checked Attached to: Host-Only Adapter Name: vboxnet0 (NOTE: this should be the name of the network you created in the previous steps)
Click OK