How to try and catch block is covered in Salesforce Testing?

There is no way to get Exeption in below code

String shref = ApexPages.currentPage().getURL();

That is why exception part is covering. If you will pass null value in shref then also excpetion will not come till you will not use shref variable.

If you want to cover catch in any cost try to update your code like below

public with sharing class HouseholdMemberController {

public HouseholdMemberController() {

System.debug('>>> HouseholdMemberController BEFORE shref');
try {
String shref = ApexPages.currentPage().getURL();
System.debug('>>> HouseholdMemberController shref='+shref);
if(Test.isRunningTest())
{
throw new Exception();
}

} catch (Exception e) {
System.debug('>>> ERROR ='+e);
}
}
}