When you are paid money for services rendered (be it a side job or full time job), you are either an employee or an independent contractor.
Employees are issued W2s with social security/medicare and income taxes withheld.
Independent contractors are self employed people and are issued a 1099MISC with earnings in Box 7 - non employee compensation, no taxes have been withheld and they report their self employment income and expenses on Schedule C to compute the amount of social security/medicare and income taxes that need to be paid on those earnings.
Sounds like these companies that hired your spouse paid them as an independent contractor, rather than an employee.
Its important to clarify with a company when you begin working for them if they classify you as an employee (employees fill out W4 forms for employers to know how much tax to withhold) or an independent contractor (generally you would fill out a W9, giving the company your name/.address/SSN to issue the 1099MISC).
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