This is possible but only happens in unusual cases as there are misaligned incentives for them. It can occur when banks have covered other banks loans and then the banks themselves have gone bankrupt, such as the recent case in Iceland. Here the remaining bank may have debt from one of their loans and equity in the same business as a legacy of a now bankrupt bank whose books they now control. In this case internal Chinese Walls may be required from a corporate governance view.
To understand this consider the below:
Debt holders lend the firm money and will receive interest on the loan. Some loans are held against assets and if the business goes under those with debt can gain some of their money back (depending on how the assets are sold and how they are prioritised versus other debt holders). In addition they receive interest on their loan. In general as they receive regular interest paying off the debt they prefer a firm to be more risk averse as they have no benefit from growth.
Equity holders buy a stake in the business, and as such receive a portion of the profits in dividends, and also the benefit of the firm increasing in value (as their stake will be worth more). However if the firm goes under they lose everything. Hence in general they are less risk averse as they would prefer more growth in the company, and if the company is in trouble they would take a punt at a big growth strategy rather than just keeping the firm alive.
As such these typo groups have differing incentives on how they would like the firm to behave and so one would not generally choose to be in both groups.