Change your LInQ little bit and you will get the result:
var query = from ce in entities.CompanyExecutives
join exec in entities.Executives on ce.ExecutiveID equals exec.ExecutiveID
join companies in entities.Companies on ce.CompanyID equals companies.CompanyID
select new
{
CompanyName = companies.CompanyName,
ExecutiveName = exec.ExecutiveName,
ExecutiveType = ce.ExecutiveType,
DateAppointment = ce.DateAppointment,
DateResignation = ce.DateResignation
};