There is no option for Employee Deduction to post to an Expense account.  Under Settings > Payroll Settings > Preferences, I scroll down to "Other Liability & Asset Accounts" where the Health Insurance Premium is located. It only lists Liability accounts so the Employee's Health Insurance Payable grows. 

Similarly, Company Contributions only have Expense accounts but the company contribution from each paycheck goes to the same Health Insurance Liability as the Employees Deduction.  So my company contribution automatically duplicates the general health insurance expense.

First of Month - I pay full insurance expense

Paycheck  - Employee deducted share of insurance from paycheck, posts to Wages expense account and Insurance Payable Liability account. Company Contribution posts to same Insurance Payable Liability account and to a Company Contributions expense account (duplicating the health insurance expense I paid at the first of the month).

Is the only option to do a journal entry after every paycheck with the following:

Debit Health Insurance Liability and Credit Health Insurance Expense for the employee and company contributions?  Then the main Health Insurance expense account only shows the remaining expense (owner's health insurance). Then under Payroll expense, is has Company Contributions and then Wages (which includes employee's deduction).

Then the liability accumulating both