tables inheritance stored procedure

create table CustomerTypes(
CustomerTypeID int primary key identity(1,1),
CustomerType varchar(11)
);


insert into CustomerTypes(CustomerTypeID,CustomerType
select 1, 'Regular' union all
select 2, 'Business'


create table Customers(
ContactID int primary key identity(1,1),
CustomerTypeID int references CustomerTypes(CustomerTypeID),
FirstName varchar(25)not null,
LastName varchar(25)not null,
DOB date not null,
Telephone varchar(18),
Notes varchar(250),
AddDate date not null
constraint cust_AltPK unique (ContactID,CustomerTypeID)
); 


create table Regular_Customer(
ContactID int primary key identity(1,1),
CustomerTypeID as 1 persisted, --regular
Specification varchar(45),
Date_Joined date,
foreign key (ContactID,CustomerTypeID) references Customers(ContactID,CustomerTypeID)
);

create table Business_Customer(
ContactID int primary key identity(1,1),
CustomerTypeID as 2 persisted, --Business
Business_Name varchar(30)not null,
Business_Type varchar(30),    
foreign key (ContactID,CustomerTypeID) references Customers(ContactID,CustomerTypeID)
);   

 create procedure CustReg
    @custType varchar(11),  
    @custTypeID int,
    @firtName varchar(25),
    @lastName varchar(25),
    @dob date,
    @telephone varchar(18),
    @notes varchar(250),
    @addDate date 
    AS
    BEGIN

    SET NOCOUNT ON

    --SET IDENTITY_INSERT CustomerTypes ON

   INSERT INTO CustomerTypes values(@custType)
        SELECT 1,'Regular'union all
        select 2, 'Business'

           --SET @CustTypeID = SCOPE_IDENTITY()
          --SET IDENTITY_INSERT CustomerTypes OFF

           DECLARE @ContactID int

           INSERT INTO 
    Customers(CustomerTypeID,FirstName,LastName,DOB,Telephone,Notes,AddDate)
           VALUES(@CustTypeID,@firtName,@lastName,@dob,@telephone,@notes,@addDate)

           SET @ContactID = SCOPE_IDENTITY()
       end  


    exec CustRegistration 'Business','5','Jean','Bruno','2012-03-09','073098743','business trip','2017-07-04'

After running exec CustRegistrationthe Customer table is populated with 5 in CustomerTypeID column. I was excepting to get a warning message of foreign key conflict in table customerType. What am I doing wrong?