Seems to me that you need one table where you have two. The same table can be your "index" (join table) and also be your reservations table. Host Families would then be put in place of Host Reservation in your data model.
Yes, I've tried it.
My problem is I don't know how to associate "student subscription" with the specific Host-Family ID.
In "HOST_RESERVATION" Table Field "ID_HOST_FAMILIES" must contain ID from "HOST_FAMILIES" Table.
How could it be done?
There are many options. The typical method is to place this field in the portal row and format it with a "use values from field" value list of ID's and family names. You select the family by name, but the value list enters the ID.