The dynamic structure factor of materials is proportional to their linear electronic response and it displays their excitation spectra. Usually the response is measured on the same length scale as the perturbation. Here we illustrate that much can be gained by studying also the mixed dynamic structure factor, which connects different spatial components of perturbation and response. We extend state-of-the-art ab initio calculations to access the mixed dynamic structure factor, including excitonic effects. Using bulk silicon and lithium fluoride as prototype examples, we show that these effects play a crucial role above and below the quasi-particle gap, and are needed in order to explain coherent inelastic x-ray scattering experiments. Our approach also yields important information concerning the microscopic structure of time-dependent density functional theory. One of the key concepts in condensed matter theory is screening, the modification of a potential felt by a charge due to the rearrangement of other charges [1]. In many cases the dominant contribution to this phenomenon can be described in linear response [2]. This means that the knowledge of the response of a system to an external perturbation is entirely contained in the density-density response function χ,which is determined only by the material.The poles of χ in frequency space are the excitation energies of the system. The density-density response function is measured directly or indirectly in many spectroscopy experiments [3], such as electron energy loss spectroscopy (EELS) [4], optical absorption [5, 6], or inelastic x-ray scattering (IXS) [7], which yields the dynamic structure factor (DSF) that is proportional to the imaginary part of χ. Knowing χ can also help to understand or predict effects such as a significant local rearrangement of charges as response of the system to a perturbation, which can have dramatic effects on the structure, for example self-trapped excitons [8]. Finally, screening is also one of the fundamental processes that govern the behavior of all many-body systems. Therefore it appears naturally as a building block in the formulation of many-body perturbation theory [9], via the screened Coulomb interaction W = v c + v c χv c , where v c is the bare Coulomb interaction. The widely-used GW approximation (GWA) [10], for example, uses W as effective interaction. Some important features of the frequency-dependent screening are captured for the homogeneous electron gas by the Lindhard dielectric function [11] from the random phase approximation (RPA) [12], where only the classical electrostatic potential between charges is taken into account. For small momentum transfer this is sufficient to describe the long-range collective oscillations of the electron gas, called plasmons, even for simple metals and semiconductors (see, e.g., [13-17]). However, in many other cases this approximation yields unsatisfactory results. Prominent examples are materials with localized d-or f-states [18-21], or loss spectra for larger momentum transfer [22-25], where a shorter length scale is probed. Moreover, the RPA cannot yield bound ex-citons [26], which are most clearly seen in optical spectra [27, 28]. Such many-body effects are instead captured by the Bethe-Salpeter equation (BSE) [29], a two-body Dyson equation that correlates the excited electrons and holes [26, 30]. This equation has been successfully used to calculate optical spectra in the framework of semi-empirical calculations since the eighties [31-34], and in first principles calculations since the nineties [35-38]. Loss spectra for vanishing momentum transfer have been looked at more recently [39-41], and a few calculations exist for loss spectra at non-vanishing momentum transfer [42-50]. Optics, EELS and IXS probe the response of the system on the same length scale as the perturbation. Besides the spectroscopic information, this allows one also to reconstruct charge excitations as an averaged function of space and time from experimental IXS spectra [51-55]. However, in an inhomogeneous material even a spatially monochromatic perturbation creates a response on different length scales [56, 57], depending on the local structure of the material. Only when all these components of the response are known can one describe induced charges with spatial resolution, and can one determine important many-body effects that depend on all the components of W. For these reasons, it is highly desirable to extend state-of-the-art advanced theoretical and numerical approaches to the description of the full inhomogeneous response of materials including excitonic effects. This gives access to the mixed DSF (MDSF), which is a matrix in reciprocal space whose diagonal is the ordinary DSF [7]. The MDSF can be measured by coherent IXS (CIXS) [7]. On the theory side, some off-diagonal elements of the MDSF in silicon were calculated in the adiabatic local density approximation (ALDA) of time-dependent den