Contacts and organizations are part of Business Foundation in Commerce. Specifically, you should use the BusinessManager API. The trick is to associate the address with the organization key. See the following example:
var billingAddress = CustomerAddress.CreateInstance();
billingAddress.AddressType = CustomerAddressTypeEnum.Billing;
billingAddress.Line1 = "Some street";
billingAddress.City = "Some city";
billingAddress.OrganizationId = organization.PrimaryKeyId;
Thanks Johan. That works.