In the US every employer that employs 4 or more people (in some states 1 or more) is required to participate in mandatory unemployment insurance (UI) and quarterly report the total number of people and total wages paid. These figures serve to calculate the unemployment insurance rates, but also provide near census-quality employment statistics known as ES-202 (http://www.bls.gov/cew/), which are used by a host of government agencies, such as BLS or BEA.
The ES-202 does not report on the number of hours worked (some states supplement that information with surveys), so it is hard to tell part-time from full-time employment. Some indication can be provided by changes in average wages (i.e. total wages paid divided by average employment) the down drift of that average may indicate increased reliance hiring more part timers, but it also may be caused by other factors (such as deskilling).
Thus, employment figures reported in the US are independent of unemployment claims - the latter being a function of eligibility. I am reasonably certain that this is the case of other developed countries as well (most have some form of administrative employment records). Some indication of the changes in the structure of the labor force may be gained by comparing employment, economically active population (which includes unemployed and self-employed, but not those outside the labor force, e.g. housewives), and the productive age population (usually between 16 and 65 years of age).
Wojtek